Beginning Algebra, 11th Edition

Notice that 0, and 1 cannot be solutions. Otherwise a denominator will equal 0.

The LCD is

Multiply by

the LCD.

Step 2 Divide out the common factors.

Distributive property

Subtract x.

Subtract 2.

Step 3 The proposed solution is which does not make any denominator equal 0.

CHECK Original equation

Let

Apply the exponents.

✓ True

The solution set is NOW TRY

Solving an Equation with Rational Expressions

Solve, and check the proposed solution.

2 m

1 m + 221 m- 22

+

1

m- 2

=

2

m+ 2

2 m

m^2 - 4

+

1

m- 2

=

2

m+ 2

EXAMPLE 5

5 - 26.

1

3

=

1

3

2

4 + 2

^1

4 - 1

x=-2.

2

1 - 222 - 1 - 22

^1

1 - 222 - 1

2

x^2 - x

=

1

x^2 - 1

- 2,

x=- 2

x+ 2 = 0

2 x+ 2 =x

21 x+ 12 =x

x 1 x+ 121 x- 12

2

x 1 x- 12

=x 1 x+ 121 x- 12

1

1 x+ 121 x- 12

x 1 x+ 121 x- 12.

2

x 1 x- 12

=

1

1 x+ 121 x- 12

1,

SECTION 7.6 Solving Equations with Rational Expressions 459

NOW TRY
EXERCISE 4
Solve, and check the proposed
solution.

3

2 x^2 - 8 x

=

1

x^2 - 16

NOW TRY ANSWERS

4. 5 - 126

NOW TRY
EXERCISE 5
Solve, and check the proposed
solution.

2 y

y^2 - 25

=

8

y+ 5

• 
  

1

y- 5

5. 596

Factor the first denominator

on the left to find the LCD,

1 m+ 221 m- 22.

Notice that and 2 cannot be solutions of this equation.

Multiply by the LCD.

Distributive property

Divide out the common factors.

Combine like terms; distributive property

Subtract 2m.

m=- 6 Subtract 2.

m+ 2 =- 4

3 m+ 2 = 2 m- 4

2 m +m+ 2 = 21 m- 22

= 1 m + 221 m- 22

2

m+ 2

1 m+ 221 m- 22

2 m

1 m+ 221 m - 22

+ 1 m+ 221 m- 22

1

m- 2

= 1 m+ 221 m- 22

2

m+ 2

1 m+ 221 m- 22 a

2 m

1 m+ 221 m- 22

+

1

m- 2

b

- 2

A check verifies that 5 - 66 is the solution set. NOW TRY