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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 8.45. (page 924)

Divide: $\frac{c + 3}{5 - c} 梅 \frac{c^{2} - 9}{c - 5}$

Short Answer

Expert verified

The required answer is $- \frac{1}{c - 3}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{c + 3}{5 - c} 梅 \frac{c^{2} - 9}{c - 5}$

02

Step 2. Simplify the expression.

$\frac{c + 3}{5 - c} 梅 \frac{c^{2} - 9}{c - 5}$

Rewrite the division as the product of the first rational expression and the reciprocal of the second.

$\frac{c + 3}{5 - c} 路 \frac{c - 5}{c^{2} - 9}$

Factor the numerators and denominators and then multiply.

$\frac{c + 3}{5 - c} 路 \frac{c - 5}{(c + 3) (c - 3)} (- 1) \frac{(c + 3) (c - 5)}{(5 - c) (c + 3) (c - 3)}$

Simplify by dividing out common factors.

$- \frac{1}{c - 3}$

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Most popular questions from this chapter

Electronics The resistance of a circuit formed by connecting two resistors in parallel is $\frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}}}$ .

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