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H. Algebra 2 9.4 notes – Rational Expressions Warm Up: Evaluate. 2 3 1. = 3 7 4 5 = 9 12 3. Factor each expression. 5. x 2 81 2. 3 8 = 4 15 4. 9 3 = 10 10 6. x 2 16x 36 Simplifying Rational Expressions. To simplify a rational expression, divide the numerator and the denominator by a common factor. Simplify x 2 5x 6 = x 2 36 Simplify b 2 49 = b 2 8b 7 Multiplying Rational Expressions. It’s just like multiplying fractions! Simplify 3 4 x 3 14 = 4 x 2 21 4 x 5 Simplify Simplify 28 4a 5 3 = 3 4a 21 49a 4 x 1 x2 x 6 = x 2 2x 3 x 2 2x 3 Simplify x 2 25 x2 4 = x 2 5 x 6 x 2 2 x 15 Simplify x 2 4 x 12 x 2 2x 35 = x 2 11x 30 x4 Simplify x2 4x 5 x2 4 = x 2 3x 2 x 2 3x 10 Dividing Rational Expressions. …Same as fraction rules! 6 12 Simplify 3 5 = x x 2r 2 2s2 Simplify 2rs = s r Simplify x 2 25 x5 = 2 2 x 2x 3 x 3x 18 Simplify Simplify x4 x 2 3x 4 = (x 2) 2 x2 4 2x 2 2x x 2 x 2 = 2 x2 9 x 2x 3 Simplify 4 x 2 20x x5 = 2 2 x 6x 9 x 9 Complex Fractions A complex fraction is a quotient that contains one or more fractions in the numerator, the denominator, or both. 4a 2 1 2 Simplify the complex fraction a 4 = 2a 1 a2 (x 2) 2 Simplify the complex fraction x2 3 = x 4 (x 3) 2 b2 4 2 Simplify the complex fraction b 2b 1 = b2 b 1 x2 4x 3 2 Simplify the complex fraction x2 6x 8 = x 9x 18 x 2 7x 10 Practice: Simplify each expression. x2 x2 x2 1. = x 5 x 1 x5 1 x 2. x 2 3 = x x7 x7 x3 4. x 1 1 = x(x 1) x 2x 3 x 1 = 3. 3x x 1 2x 3 5. 3x 3 6 y 5 = 5 y 2 4x5 6. x 2 5 x 6 x 2 3x 2 x2 2x 3