1. 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

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

3. 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)

4. Example 2 • 135x7y3 45x5y5 Step 2: Factor and cancel common factors.
Simplify: 5x2y x5
3xy x4y •
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

5. Example 3 • 5x(4 – x ) (x – 1)(x + 4) • x(x – 1) (x + 4)(x – 4)
Simplify: 20x – 5x 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

6. Example 4 • x – 4 • (x + 2)(x2 – 2x + 4) 1
Simplify: x – (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)

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

8. 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