7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (2024)

Learning Objectives

By the end of this section, you will be able to:

  • Solve rational equations
  • Use rational functions
  • Solve a rational equation for a specific variable

Be Prepared 7.10

Before you get started, take this readiness quiz.

Solve: 16x+12=13.16x+12=13.
If you missed this problem, review Example 2.9.

Be Prepared 7.11

Solve: n25n36=0.n25n36=0.
If you missed this problem, review Example 6.45.

Be Prepared 7.12

Solve the formula 5x+2y=105x+2y=10 for y.y.
If you missed this problem, review Example 2.31.

After defining the terms ‘expression’ and ‘equation’ earlier, we have used them throughout this book. We have simplified many kinds of expressions and solved many kinds of equations. We have simplified many rational expressions so far in this chapter. Now we will solve a rational equation.

Rational Equation

A rational equation is an equation that contains a rational expression.

You must make sure to know the difference between rational expressions and rational equations. The equation contains an equal sign.

Rational ExpressionRational Equation18x+12y+6y2361n3+1n+418x+12=14y+6y236=y+11n3+1n+4=15n2+n12Rational ExpressionRational Equation18x+12y+6y2361n3+1n+418x+12=14y+6y236=y+11n3+1n+4=15n2+n12

Solve Rational Equations

We have already solved linear equations that contained fractions. We found the LCD of all the fractions in the equation and then multiplied both sides of the equation by the LCD to “clear” the fractions.

We will use the same strategy to solve rational equations. We will multiply both sides of the equation by the LCD. Then, we will have an equation that does not contain rational expressions and thus is much easier for us to solve. But because the original equation may have a variable in a denominator, we must be careful that we don’t end up with a solution that would make a denominator equal to zero.

So before we begin solving a rational equation, we examine it first to find the values that would make any denominators zero. That way, when we solve a rational equation we will know if there are any algebraic solutions we must discard.

An algebraic solution to a rational equation that would cause any of the rational expressions to be undefined is called an extraneous solution to a rational equation.

Extraneous Solution to a Rational Equation

An extraneous solution to a rational equation is an algebraic solution that would cause any of the expressions in the original equation to be undefined.

We note any possible extraneous solutions, c, by writing xcxc next to the equation.

Example 7.33

How to Solve a Rational Equation

Solve: 1x+13=56.1x+13=56.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (1)7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (2)7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (3)7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (4)7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (5)

Try It 7.65

Solve: 1y+23=15.1y+23=15.

Try It 7.66

Solve: 23+15=1x.23+15=1x.

The steps of this method are shown.

How To

Solve equations with rational expressions.

  1. Step 1. Note any value of the variable that would make any denominator zero.
  2. Step 2. Find the least common denominator of all denominators in the equation.
  3. Step 3. Clear the fractions by multiplying both sides of the equation by the LCD.
  4. Step 4. Solve the resulting equation.
  5. Step 5.

    Check:

    • If any values found in Step 1 are algebraic solutions, discard them.
    • Check any remaining solutions in the original equation.

We always start by noting the values that would cause any denominators to be zero.

Example 7.34

How to Solve a Rational Equation using the Zero Product Property

Solve: 15y=6y2.15y=6y2.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (6)
Note any value of the variable that would make
any denominator zero.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (7)
Find the least common denominator of all denominators in
the equation. The LCD is y2.
Clear the fractions by multiplying both sides of
the equation by the LCD.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (8)
Distribute.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (9)
Multiply.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (10)
Solve the resulting equation. First
write the quadratic equation in standard form.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (11)
Factor.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (12)
Use the Zero Product Property.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (13)
Solve.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (14)
Check.
We did not get 0 as an algebraic solution.


7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (15)
The solution is y=2,y=2, y=3.y=3.

Try It 7.67

Solve: 12x=15x2.12x=15x2.

Try It 7.68

Solve: 14y=12y2.14y=12y2.

In the next example, the last denominators is a difference of squares. Remember to factor it first to find the LCD.

Example 7.35

Solve: 2x+2+4x2=x1x24.2x+2+4x2=x1x24.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (16)
Note any value of the variable
that would make any denominator
zero.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (17)
Find the least common
denominator of all denominators
in the equation.
The LCD is (x+2)(x2).(x+2)(x2).
Clear the fractions by multiplying
both sides of the equation by the
LCD.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (18)
Distribute.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (19)
Remove common factors.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (20)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (21)
Distribute.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (22)
Solve.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (23)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (24)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (25)
Check:
We did not get 2 or −2 as algebraic solutions.

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (26)
The solution is x=−1.x=−1.

Try It 7.69

Solve: 2x+1+1x1=1x21.2x+1+1x1=1x21.

Try It 7.70

Solve: 5y+3+2y3=5y29.5y+3+2y3=5y29.

In the next example, the first denominator is a trinomial. Remember to factor it first to find the LCD.

Example 7.36

Solve: m+11m25m+4=5m43m1.m+11m25m+4=5m43m1.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (27)
Note any value of the variable that
would make any denominator zero.
Use the factored form of the quadratic
denominator.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (28)
Find the least common denominator
of all denominators in the equation.
The LCD is (m4)(m1).(m4)(m1).
Clear the fractions by
multiplying both sides of the
equation by the LCD.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (29)
Distribute.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (30)
Remove common factors.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (31)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (32)
Solve the resulting equation.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (33)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (34)
Check.
The only algebraic solution
was 4, but we said that 4 would make
a denominator equal to zero. The algebraic solution is an
extraneous solution.
There is no solution to this equation.

Try It 7.71

Solve: x+13x27x+10=6x54x2.x+13x27x+10=6x54x2.

Try It 7.72

Solve: y6y2+3y4=2y+4+7y1.y6y2+3y4=2y+4+7y1.

The equation we solved in the previous example had only one algebraic solution, but it was an extraneous solution. That left us with no solution to the equation. In the next example we get two algebraic solutions. Here one or both could be extraneous solutions.

Example 7.37

Solve: yy+6=72y236+4.yy+6=72y236+4.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (35)
Factor all the denominators,
so we can note any value of
the variable that would make
any denominator zero.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (36)
Find the least common denominator.
The LCD is (y6)(y+6).(y6)(y+6).
Clear the fractions.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (37)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (38)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (39)
Solve the resulting equation.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (40)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (41)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (42)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (43)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (44)
Check.

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (45)
The solution is y=4.y=4.

Try It 7.73

Solve: xx+4=32x216+5.xx+4=32x216+5.

Try It 7.74

Solve: yy+8=128y264+9.yy+8=128y264+9.

In some cases, all the algebraic solutions are extraneous.

Example 7.38

Solve: x2x223x+3=5x22x+912x212.x2x223x+3=5x22x+912x212.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (46)
We will start by factoring all
denominators, to make it easier
to identify extraneous solutions and the LCD.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (47)
Note any value of the variable
that would make any denominator zero.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (48)
Find the least common
denominator.
The LCD is 12(x1)(x+1).12(x1)(x+1).
Clear the fractions.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (49)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (50)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (51)
Solve the resulting equation.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (52)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (53)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (54)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (55)
Check.

x=1x=1 and x=−1x=−1 are extraneous solutions.
The equation has no solution.

Try It 7.75

Solve: y5y1053y+6=2y219y+5415y260.y5y1053y+6=2y219y+5415y260.

Try It 7.76

Solve: z2z+834z8=3z216z168z2+16z64.z2z+834z8=3z216z168z2+16z64.

Example 7.39

Solve: 43x210x+3+33x2+2x1=2x22x3.43x210x+3+33x2+2x1=2x22x3.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (56)
Factor all the denominators, so we can note any value of the variable that would make any denominator
zero.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (57)
x1,x13,x3x1,x13,x3
Find the least common denominator. The LCD is (3x1)(x+1)(x3).(3x1)(x+1)(x3).
Clear the fractions.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (58)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (59)
Distribute.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (60)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (61)
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (62)
The only algebraic solution was x=3,x=3, but we said that x=3x=3 would make a denominator equal to zero. The algebraic solution is an extraneous solution.
There is no solution to this equation.

Try It 7.77

Solve: 15x2+x63x2=2x+3.15x2+x63x2=2x+3.

Try It 7.78

Solve: 5x2+2x33x2+x2=1x2+5x+6.5x2+2x33x2+x2=1x2+5x+6.

Use Rational Functions

Working with functions that are defined by rational expressions often lead to rational equations. Again, we use the same techniques to solve them.

Example 7.40

For rational function, f(x)=2x6x28x+15,f(x)=2x6x28x+15, find the domain of the function, solve f(x)=1,f(x)=1, and find the points on the graph at this function value.

Solution

The domain of a rational function is all real numbers except those that make the rational expression undefined. So to find them, we will set the denominator equal to zero and solve.

x28x+15=0x28x+15=0
Factor the trinomial.(x3)(x5)=0(x3)(x5)=0
Use the Zero Product Property.x3=0x5=0x3=0x5=0
Solve.x=3x=5x=3x=5
The domain is all real numbers except x3,x5.x3,x5.


7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (63)
Substitute in the rational expression.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (64)
Factor the denominator.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (65)
Multiply both sides by the LCD,
(x3)(x5).(x3)(x5).
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (66)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (67)
Solve.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (68)
Factor.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (69)
Use the Zero Product Property.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (70)
Solve.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (71)

However, x=3x=3 is outside the domain of this function, so we discard that root as extraneous.

The value of the function is 1 when x=7.x=7. So the points on the graph of this function when f(x)=1f(x)=1 is (7,1))(7,1))

Try It 7.79

For rational function, f(x)=8xx27x+12,f(x)=8xx27x+12, find the domain of the function solve f(x)=3f(x)=3 find the points on the graph at this function value.

Try It 7.80

For rational function, f(x)=x1x26x+5,f(x)=x1x26x+5, find the domain of the function solve f(x)=4f(x)=4 find the points on the graph at this function value.

Solve a Rational Equation for a Specific Variable

When we solved linear equations, we learned how to solve a formula for a specific variable. Many formulas used in business, science, economics, and other fields use rational equations to model the relation between two or more variables. We will now see how to solve a rational equation for a specific variable.

When we developed the point-slope formula from our slope formula, we cleared the fractions by multiplying by the LCD.

m=yy1xx1Multiply both sides of the equation byxx1.m(xx1)=(yy1xx1)(xx1)Simplify.m(xx1)=yy1Rewrite the equation with theyterms on the left.yy1=m(xx1)m=yy1xx1Multiply both sides of the equation byxx1.m(xx1)=(yy1xx1)(xx1)Simplify.m(xx1)=yy1Rewrite the equation with theyterms on the left.yy1=m(xx1)

In the next example, we will use the same technique with the formula for slope that we used to get the point-slope form of an equation of a line through the point (2,3).(2,3). We will add one more step to solve for y.

Example 7.41

Solve:m=y2x3m=y2x3 for y.y.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (72)
Note any value of the variable that would
make any denominator zero.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (73)
Clear the fractions by multiplying both sides of
the equation by the LCD, x3.x3.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (74)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (75)
Isolate the term with y.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (76)

Try It 7.81

Solve: m=y5x4m=y5x4for y.y.

Try It 7.82

Solve: m=y1x+5m=y1x+5 for y.y.

Remember to multiply both sides by the LCD in the next example.

Example 7.42

Solve: 1c+1m=11c+1m=1 for c.

Solution

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (77)
Note any value of the variable that would make
any denominator zero.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (78)
Clear the fractions by multiplying both sides of
the equations by the LCD, cm.
7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (79)
Distribute.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (80)
Simplify.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (81)
Collect the terms with c to the right.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (82)
Factor the expression on the right.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (83)
To isolate c, divide both sides by m1.m1.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (84)
Simplify by removing common factors.7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (85)
Notice that even though we excluded c=0,m=0c=0,m=0 from the original equation, we must also now state that m1.m1.

Try It 7.83

Solve: 1a+1b=c1a+1b=c for a.

Try It 7.84

Solve: 2x+13=1y2x+13=1y for y.

Media

Access this online resource for additional instruction and practice with equations with rational expressions.

  • Equations with Rational Expressions

Section 7.4 Exercises

Practice Makes Perfect

Solve Rational Equations

In the following exercises, solve each rational equation.

197.

1 a + 2 5 = 1 2 1 a + 2 5 = 1 2

198.

6 3 2 d = 4 9 6 3 2 d = 4 9

199.

4 5 + 1 4 = 2 v 4 5 + 1 4 = 2 v

200.

3 8 + 2 y = 1 4 3 8 + 2 y = 1 4

201.

1 2 m = 8 m 2 1 2 m = 8 m 2

202.

1 + 4 n = 21 n 2 1 + 4 n = 21 n 2

203.

1 + 9 p = −20 p 2 1 + 9 p = −20 p 2

204.

1 7 q = −6 q 2 1 7 q = −6 q 2

205.

5 3 v 2 = 7 4 v 5 3 v 2 = 7 4 v

206.

8 2 w + 1 = 3 w 8 2 w + 1 = 3 w

207.

3 x + 4 + 7 x 4 = 8 x 2 16 3 x + 4 + 7 x 4 = 8 x 2 16

208.

5 y 9 + 1 y + 9 = 18 y 2 81 5 y 9 + 1 y + 9 = 18 y 2 81

209.

8 z 10 7 z + 10 = 5 z 2 100 8 z 10 7 z + 10 = 5 z 2 100

210.

9 a + 11 6 a 11 = 6 a 2 121 9 a + 11 6 a 11 = 6 a 2 121

211.

−10 q 2 7 q + 4 = 1 −10 q 2 7 q + 4 = 1

212.

2 s + 7 3 s 3 = 1 2 s + 7 3 s 3 = 1

213.

v 10 v 2 5 v + 4 = 3 v 1 6 v 4 v 10 v 2 5 v + 4 = 3 v 1 6 v 4

214.

w + 8 w 2 11 w + 28 = 5 w 7 + 2 w 4 w + 8 w 2 11 w + 28 = 5 w 7 + 2 w 4

215.

x 10 x 2 + 8 x + 12 = 3 x + 2 + 4 x + 6 x 10 x 2 + 8 x + 12 = 3 x + 2 + 4 x + 6

216.

y 5 y 2 4 y 5 = 1 y + 1 + 1 y 5 y 5 y 2 4 y 5 = 1 y + 1 + 1 y 5

217.

b + 3 3 b + b 24 = 1 b b + 3 3 b + b 24 = 1 b

218.

c + 3 12 c + c 36 = 1 4 c c + 3 12 c + c 36 = 1 4 c

219.

d d + 3 = 18 d 2 9 + 4 d d + 3 = 18 d 2 9 + 4

220.

m m + 5 = 50 m 2 25 + 6 m m + 5 = 50 m 2 25 + 6

221.

n n + 2 3 = 8 n 2 4 n n + 2 3 = 8 n 2 4

222.

p p + 7 8 = 98 p 2 49 p p + 7 8 = 98 p 2 49

223.

q 3 q 9 3 4 q + 12 = 7 q 2 + 6 q + 63 24 q 2 216 q 3 q 9 3 4 q + 12 = 7 q 2 + 6 q + 63 24 q 2 216

224.

r 3 r 15 1 4 r + 20 = 3 r 2 + 17 r + 40 12 r 2 300 r 3 r 15 1 4 r + 20 = 3 r 2 + 17 r + 40 12 r 2 300

225.

s 2 s + 6 2 5 s + 5 = 5 s 2 3 s 7 10 s 2 + 40 s + 30 s 2 s + 6 2 5 s + 5 = 5 s 2 3 s 7 10 s 2 + 40 s + 30

226.

t 6 t 12 5 2 t + 10 = t 2 23 t + 70 12 t 2 + 36 t 120 t 6 t 12 5 2 t + 10 = t 2 23 t + 70 12 t 2 + 36 t 120

227.

2 x 2 + 2 x 8 1 x 2 + 9 x + 20 = 4 x 2 + 3 x 10 2 x 2 + 2 x 8 1 x 2 + 9 x + 20 = 4 x 2 + 3 x 10

228.

5 x 2 + 4 x + 3 + 2 x 2 + x 6 = 3 x 2 x 2 5 x 2 + 4 x + 3 + 2 x 2 + x 6 = 3 x 2 x 2

229.

3 x 2 5 x 6 + 3 x 2 7 x + 6 = 6 x 2 1 3 x 2 5 x 6 + 3 x 2 7 x + 6 = 6 x 2 1

230.

2 x 2 + 2 x 3 + 3 x 2 + 4 x + 3 = 6 x 2 1 2 x 2 + 2 x 3 + 3 x 2 + 4 x + 3 = 6 x 2 1

Solve Rational Equations that Involve Functions

231.

For rational function, f(x)=x2x2+6x+8,f(x)=x2x2+6x+8, find the domain of the function solve f(x)=5f(x)=5 find the points on the graph at this function value.

232.

For rational function, f(x)=x+1x22x3,f(x)=x+1x22x3, find the domain of the function solve f(x)=1f(x)=1 find the points on the graph at this function value.

233.

For rational function, f(x)=2xx27x+10,f(x)=2xx27x+10, find the domain of the function solve f(x)=2f(x)=2 find the points on the graph at this function value.

234.

For rational function, f(x)=5xx2+5x+6,f(x)=5xx2+5x+6,
find the domain of the function
solve f(x)=3f(x)=3
the points on the graph at this function value.

Solve a Rational Equation for a Specific Variable

In the following exercises, solve.

235.

Cr=2πCr=2π for r.r.

236.

Ir=PIr=P for r.r.

237.

v+3w1=12v+3w1=12 for w.w.

238.

x+52y=43x+52y=43 for y.y.

239.

a=b+3c2a=b+3c2 for c.c.

240.

m=n2nm=n2n for n.n.

241.

1p+2q=41p+2q=4 for p.p.

242.

3s+1t=23s+1t=2 for s.s.

243.

2v+15=3w2v+15=3w for w.w.

244.

6x+23=1y6x+23=1y for y.y.

245.

m+3n2=45m+3n2=45 for n.n.

246.

r=s3tr=s3t for t.t.

247.

Ec=m2Ec=m2 for c.c.

248.

RT=WRT=W for T.T.

249.

3x5y=143x5y=14 for y.y.

250.

c=2a+b5c=2a+b5 for a.a.

Writing Exercises

251.

Your class mate is having trouble in this section. Write down the steps you would use to explain how to solve a rational equation.

252.

Alek thinks the equation yy+6=72y236+4yy+6=72y236+4 has two solutions, y=−6y=−6 and y=4.y=4. Explain why Alek is wrong.

Self Check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (86)

On a scale of 110,110, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

7.4 Solve Rational Equations - Intermediate Algebra 2e | OpenStax (2024)
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