11.4 Multiply and Divide Rational Expressions

SIMPLIFYING RATIONAL EXPRESSIONS Step 1: Factor numerator and denominator “when in doubt, write it out!!” Step 2: Cross out common factors Step 3: Simplified form

Simplify Assume the denominator cannot equal zero.

Example 1 Simplify a rational expression x² + 7x + 10 x² - 4 Step 1: Factor numerator and denominator (x² + 7x + 10) = (x+2)(x+5) (x² - 4) (x+2)(x-2) Step 2: Cross out common factor (x+2)(x+5) (x+2)(x-2) Step 3: Simplified Form x + 5 x - 2

Checkpoint Simplify the expression 1. x² - 2x – 15 x² + 4x + 3 (x – 5)(x + 3) (x + 1)(x + 3) x – 5 x + 1

Multiply the fractions Reduce before multiply.

Multiply the fractions Reduce before multiply.

Example 2 Multiply rational expressions Step 1: Factor and Multiply

Checkpoint Multiply the expression 6x² + 18x x² - x – 2 x² + x – 6 * x² - 7x – 8 6x(x + 3)(x-2)(x+1) (x+3)(x-2)(x-8)(x+1) 6x x-8

More Examples  Multiply the expressions. Simplify the result.

Divide the Rational Expressions You can only Reduce when Multiplying

Example 4 Divide rational expressions Step 1: Multiply by reciprocal 3 x² + 6x – 7 x+7 * 8x² - 8x Step 2: Factor and Multiply 3 (x+7)(x-1) (x+7)(8x)(x-1)

More Examples  Divide each expression. Simplify the result.

Checkpoint Divide the expression 3. (x – 5) (2x² - 5x + 2) (9x² - 18x)(2x² - 11x + 5) (x – 5)(2x-1)(x-2) 9x(x–2)(2x-1)(x-5) 1_ 9x