Beginning Algebra, 11th Edition

Solving an Equation with Rational Expressions

Solve, and check the proposed solution(s).

1

x- 1

+

1

2

=

2

1 x+ 121 x- 12

1

x- 1

+

1

2

=

2

x^2 - 1

EXAMPLE 6

460 CHAPTER 7 Rational Expressions and Applications

NOW TRY
EXERCISE 6
Solve, and check the proposed
solution(s).

3

m^2 - 9

=

1

21 m- 32

• 
  

1

4

NOW TRY ANSWER

6. 5 - 16

Distributive property

21 x+ 121 x- 12

2

1 x+ 121 x- 12

21 x+ 121 x- 12

1

x- 1

+ 21 x+ 121 x- 12

1

2

=

Divide out the common factors.

Distributive property

Subtract 4. Combine like terms.

Factor.

or Zero-factor property

x=- 3 or x= 1 Proposed solutions

x+ 3 = 0 x - 1 = 0

1 x+ 321 x- 12 = 0

x^2 + 2 x- 3 = 0

2 x+ 2 +x^2 - 1 = 4

21 x+ 12 + 1 x+ 121 x- 12 = 4

Factor the denominator on the

right. The LCD is 2 1 x+ 121 x- 12.

Multiply by the LCD.

21 x+ 121 x- 12 a

1

x- 1

+

1

2

b= 21 x+ 121 x- 12

2

1 x+ 121 x- 12

or a

denominator is 0.

xZ1, - 1

Write in

standard form.

Since 1 makes a denominator equal 0, 1 is nota solution. Check that is a solution.

CHECK Original equation

Let

Simplify.

✓ True

The solution set is NOW TRY

Solving an Equation with Rational Expressions

Solve, and check the proposed solution.

= 41 k+ 121 k+ 32

3

41 k+ 32

41 k+ 121 k+ 32 a

1

1 k+ 121 k+ 32

+

1

21 k+ 12

b

1

1 k+ 121 k+ 32

+

1

21 k+ 12

=

3

41 k+ 32

1

k^2 + 4 k+ 3

+

1

2 k+ 2

=

3

4 k+ 12

EXAMPLE 7

5 - 36.

1

4

=

1

4

1

- 4

+

1

2

^2

9 - 1

x=-3.

1

- 3 - 1

+

1

2

^2

1 - 322 - 1

1

x- 1

+

1

2

=

2

x^2 - 1

- 3

Factor each denominator.

The LCD is 4 1 k+ 121 k+ 32.

kZ-1, - 3

Multiply by

the LCD.

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