Lesson 40. Ch 8.4 Multiply and Divide Rational Expressions Example 1. Simplify a rational expression. x 2 − 2x − 3
Simplify the expression 2
x − x− 6
•
Factor numerator and denominator. •
Divide out common factor. •
Simplified form. AVOID ERRORS. Do not divide out variable terms that are not factors. Example 2. Multiplying Rational Expressions. Multiply the expressions 2x 2 − 10x x + 3
. Simplify the results. i
x 2 − 25
2x 2
Step 1. Factor numerators and denominators. Step 2. Multiply numerators and denominators. Step 3. Divide out common factors. Step 4. Simplify/Multiply Example 3. Multiply a rational expression by a polynomial. Multiply the expressions x+5
i x 2 + x + 1 . Simplify the results. 3
x −1
(
Step 1. Write polynomial as a rational expression. Step 2. Factor denominator. Step 3. Divide out common factors. Step 4. Simplify. )
Example 4. Divide rational expressions. Divide the expressions 4x
x 2 − 2x
. Simplify the result. ÷ 2
5x − 20 x − 6x + 8
Step 1. Multiply by reciprocal. Step 2. Factor Step 3. Divide out common factors. Step 4 Simplify. Example 5. Divide rational expressions by a polynomial. 2x 2 + 3x − 5
Divide the expressions ÷ 2x 2 + 5x . Simplify the result. 6x
(Follow steps from above. See Example 4) (
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