Multiplying and Dividing Rational Expressions (11-4) Objective: Multiply and divide rational expressions.

Multiply Rational Expressions To multiply fractions, you multiply numerators and multiply denominators. Use this same method to multiply rational expressions. Let a, b, c, and d be polynomials with b  0 and d  0. Then .

Example 1 Find each product. . 7 6 7 2 3

Example 1 Find each product. .

Check Your Progress Choose the best answer for the following. Find . 2

Check Your Progress Choose the best answer for the following. Find .

Multiply Rational Expressions When you multiply fractions that involve units of measure, you can divide by the units in the same way that you divide by variables. Recall that this process is called dimensional analysis. You can use dimensional analysis to convert units of measure within a system and between systems.

Example 2 The velocity that a spacecraft must have in order to escape Earth’s gravitational pull is called the escape velocity. The escape velocity for a spacecraft leaving Earth is about 40,320 kilometers per hour. What is this speed in meters per second? 2240 5 18

Check Your Progress Choose the best answer for the following. The speed of sound, or Mach 1, is approximately 330 meters per second at sea level. What is the speed of sound in kilometers per hour? 330 kilometers per hour 1188 kilometers per hour 3300 kilometers per hour 500 kilometers per hour 66 18 5

Divide Rational Expressions To divide by a fraction, you multiply by the reciprocal. You can use this same method do divide by a rational expression. Let a, b, c, and d be polynomials with b ≠ 0, c ≠ 0, and d ≠ 0. Then .

Example 3 Find 2 5 2 4 11

Check Your Progress Choose the best answer for the following. Find . 3 9 7 3

Example 4 Find each quotient. .

Example 4 Find each quotient. .

Check Your Progress Choose the best answer for the following. Find .

Check Your Progress Choose the best answer for the following. Find .

Dividing Rational Expressions Sometimes you must factor a quadratic expression before you can simplify the quotient of rational expressions.

Example 5 Find

Check Your Progress Choose the best answer for the following. Find .