Warm-Up The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=2: x = 4, y = 3 x = 8, y = -1 x = ½, y = 12

Multiply and Divide Rational Expressions Section 8-4 Multiply and Divide Rational Expressions

Example 1 (x – 4)(x – 4) (x + 6)(x – 4) Step 2: Cancel common factors. Simplify: x2 – 8x + 16 x2 + 2x – 24 Step 1: Factor the numerator & denominator. (x – 4)(x – 4) (x + 6)(x – 4) Step 2: Cancel common factors. = (x – 4) (x + 6)

Example 2 • 135x7y3 45x5y5 Step 2: Factor and cancel common factors. Simplify: 5x2y3 27x5 3xy4 15x4y • Step 1: Multiply the numerators & denominators. 135x7y3 45x5y5 Step 2: Factor and cancel common factors. = 45 • 3 • x5 • x2 • y3 45 • x5 • y3 • y2 = 3x2 y2

Example 3 • 5x(4 – x ) (x – 1)(x + 4) • x(x – 1) (x + 4)(x – 4) Simplify: 20x – 5x2 x2 + 3x – 4 x2 – x x2 – 16 • Step 1: Factor the numerators & denominators. 5x(4 – x ) (x – 1)(x + 4) • x(x – 1) (x + 4)(x – 4) Step 2: Cancel common factors. = 5(-1)(x – 4) (x – 4) Step 3: Rewrite (4 – x) as -1(x – 4). = -5

Example 4 • x – 4 • (x + 2)(x2 – 2x + 4) 1 Simplify: x – 4 (x2 – 2x + 4) x3 + 8 • Step 1: Factor the numerators & denominators. x – 4 (x2 – 2x + 4) • (x + 2)(x2 – 2x + 4) 1 Step 2: Cancel common factors. = x – 4 x + 2 Sum and Difference of Two Cubes: (a + b)(a2 – ab + b2) (a – b)(a2 + ab + b2)

Example 5 ÷ x2 – 4x – 21 x2 – 100 5x + 15 x2 + 3x – 70 • Divide : x2 – 4x – 21 x2 + 3x – 70 5x + 15 x2 – 100 ÷ Step 1: Multiply by the reciprocal. x2 – 4x – 21 x2 – 100 5x + 15 x2 + 3x – 70 • Step 2: Factor. (x – 7)(x + 3) (x – 10)(x + 10) • (x + 10)(x – 7) 5(x + 3) = x – 10 5

Homework Section 8-4 Pages 577 –580 6 – 17, 21, 22, 24, 26, 28, 29, 30, 34, 37, 39, 40, 43, 54, 55, 61, 63