Holt McDougal Algebra 2 Adding and Subtracting Rational Expressions Adding and Subtracting Rational Expressions Holt Algebra 2Holt McDougal Algebra 2

Holt McDougal Algebra 2

Adding and Subtracting Rational ExpressionsAdding and Subtracting Rational Expressions

Holt Algebra 2Holt McDougal Algebra 2

• How do we add and subtract rational expressions?

• How do we simplify complex fractions?


Adding and Subtracting Rational Expressions

Add. Identify any x-values for which the expression is undefined.

Example 1: Add and Subtract Rational Expressions

Factor the denominators.

The LCD is (x + 2)(x – 2).

Rewrite as one fraction.

Factor the numerator.

Undefined at x = –2 and x = 2

x x + 2

+ –8 x2 – 4

8

2x 2x2xx

2

2

x

x

2 2

2

xx

x x2 8

2x 2 2

4

xx

x 4x

2x



Subtract. Identify any x-values for which the expression is undefined.Example 2: Add and Subtract Rational Expressions

Factor the denominators.

The LCD is (x 1)(x 1).


Simplify the numerator.

Factor the numerator.

1

6

1

1222

2

x

x

x

x Change the signs for subtraction.

Undefined at x = –1 and x = 1

122 2 x

1

6

x

x1x1x 1

1

x

x

1 1

122 2

xx

x 2x x x6 6

1 1

2

xx

x x7 6 1x 1 1

6

xx

x

1

6

x

x




Treat like a mixed number



5

47

x

x Change the signs for subtraction.

Undefined at x = –5

57 x5xx4

5

7

xx 35 x4

5

353

x

x




Treat like a mixed number



xx

x3

3

26

Change the signs for subtraction.

Undefined at x = 3

3xx26 33 xx

3

3 2

x

x x9 x26

3

6113 2

x

xx 1 23x x11 6 Factor the numerator.

18 112 ,9 33

3 1 3x 23 x

231 x 23 x



Lesson 6.3 Practice C

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Holt McDougal Algebra 2 Adding and Subtracting Rational Expressions Adding and Subtracting Rational Expressions Holt Algebra 2Holt McDougal Algebra 2