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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 433 (page 737)

In the following exercise, simplify
$\frac{\frac{2}{x^{2} - 49} + \frac{1}{z + 7}}{\frac{9}{z + 7} + \frac{12}{z - 7}}$

Short Answer

Expert verified

The solution is, $\frac{z - 5}{21 z + 21}$

Step by step solution

01

Step 1. Given Information

$\frac{\frac{2}{x^{2} - 49} + \frac{1}{z + 7}}{\frac{9}{z + 7} + \frac{12}{z - 7}}$

02

Step 2. Simplify.

The LCD of all fractions in the complex rational expression is $(z + 7) (z - 7)$

Multiply the numerator and denominator by the LCD.

$= \frac{(z + 7) (z - 7) (\frac{2}{x^{2} - 49} + \frac{1}{z + 7})}{(z + 7) (z - 7) (\frac{9}{z + 7} + \frac{12}{z - 7})} = \frac{((z + 7) (z - 7) \frac{2}{x^{2} - 49} + (z + 7) (z - 7) \frac{1}{z + 7})}{((z + 7) (z - 7) \frac{9}{z + 7} + (z + 7) (z - 7) \frac{12}{z - 7})} = \frac{2 + (z - 7)}{9 (z - 7) + 12 (z + 7)} = \frac{z - 5}{21 z + 21}$

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Most popular questions from this chapter

If $a$ varies directly as $b$ and $a = 16$ , when $b = 4$ . Find the equation that relates $a$ and $b$ .

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