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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 90. (page 930)

In the following exercises, multiply.
$\frac{18 c - 2 c^{2}}{6 c + 30} 路 \frac{c^{2} + 7 c + 10}{c^{2} - 81}$

Short Answer

Expert verified

The required answer is $- \frac{c (c + 2)}{3 (c + 9)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{18 c - 2 c^{2}}{6 c + 30} 路 \frac{c^{2} + 7 c + 10}{c^{2} - 81}$

02

Step 2. Simplify the expression.

$\frac{18 c - 2 c^{2}}{6 c + 30} 路 \frac{c^{2} + 7 c + 10}{c^{2} - 81}$

Factor the numerator and denominator completely,

$\frac{2 c (9 - c)}{6 (c + 5)} 路 \frac{(c + 5) (c + 2)}{(c + 9) (c - 9)}$

Multiply the numerators and denominators,

$- \frac{2 c (c - 9) (c + 5) (c + 2)}{6 (c + 5) (c + 9) (c - 9)}$

Simplify by dividing out common factors,

$- \frac{c (c + 2)}{3 (c + 9)}$

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