Beginning Algebra, 11th Edition

456 CHAPTER 7 Rational Expressions and Applications

OBJECTIVES OBJECTIVE 1 Distinguish between operations with rational expressions

and equations with terms that are rational expressions.Before solving equa-

tions with rational expressions, you must understand the difference between sums and

differences of terms with rational coefficients, or rational expressions,and equations

with terms that are rational expressions.

Sums and differences are expressions to simplify. Equations are solved.

Distinguishing between Expressions and Equations

Identify each of the following as an expressionor an equation. Then simplify the

expression or solve the equation.

(a)

This is a difference of two terms. It represents an

expressionto simplify since there is no equals symbol.

The LCD is 12. Write each coefficient with this LCD.

Multiply.

Combine like terms, using the distributive property:

(b)

Because there is an equals symbol,

this is an equationto be solved.

12 a

3

4

x-

2

3

xb= 12 a

1

2

b

3

4

x-

2

3

x=

1

2

9

12 x-

8

12 x=A

9

12 -

8

12 Bx.

=

1

12

x

=

9

12

x-

8

12

x

=

3 # 3

3 # 4

x-

4 # 2

4 # 3

x

3

4

x-

2

3

x

EXAMPLE 1

Solving Equations with Rational Expressions

7.6

1 Distinguish between

operations with

rational expressions

and equations with

terms that are

rational expressions.

2 Solve equations

with rational

expressions.

3 Solve a formula for

a specified variable.

NOW TRY
EXERCISE 1
Identify each of the following
as an expressionor an
equation.Then simplify the
expression or solve the
equation.

(a)

(b)

3

2

t-

5

7

t

3

2

t-

5

7

t=

11

7

NOW TRY ANSWERS

1. (a)equation;
   (b)expression;^1114 t

526

Use the multiplication property of

equality to clear fractions.

Multiply by 12, the LCD.

Distributive property

Multiply.

x= 6 Combine like terms.

9 x- 8 x= 6

12 a

3

4

xb - 12 a

2

3

xb= 12 a

1

2

b

CHECK Original equation

Let

Multiply.

✓ True

Since a true statement results, 566 is the solution set of the equation. NOW TRY

1

2

=

1

2

9

2

- 4 

1

2

x=6.

3

4

162 -

2

3

162 

1

2

3

4

x-

2

3

x=

1

2

Multiply

eachterm

by 12.

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