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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 8: Q 100. (page 930)

Divide Rational Expressions: $\frac{7 + x}{x - 6} \div \frac{49 - x^{2}}{x + 6}$

Short Answer

Expert verified

The required answer is $\frac{x + 6}{(x - 6) (7 - x)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is

$\frac{7 + x}{x - 6} \div \frac{49 - x^{2}}{x + 6}$

02

Step 2. Simplify the expression.

$\frac{7 + x}{x - 6} \div \frac{49 - x^{2}}{x + 6} = \frac{\frac{7 + x}{x - 6}}{\frac{49 - x^{2}}{x + 6}}$

Apply the fraction rule.

$= \frac{(7 + x) (x + 6)}{(x - 6) (49 - x^{2})} = \frac{x + 6}{(x - 6) (7 - x)}$

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