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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. 416 (page 736)

In the following exercises, perform the indicated operations
$\frac{5 q}{p^{2} q - p^{2}} + \frac{4 q}{q^{2} - 1}$

Short Answer

Expert verified

Simplified expression is $\frac{5 q^{2} + 5 q + 4 p^{2} q}{p^{2} (q^{2} - 1)}$

Step by step solution

01

Step 1. Given Information

Expression

\frac{5 q}{p^{2} q - p^{2}} + \frac{4 q}{q^{2} - 1}

02

Step 2. Find LCD

Denominator of first fraction is $p^{2} q - p^{2}$

Factorize this denominator

$p^{2} (q - 1)$

Denominator of the second fraction is $q^{2} - 1$

Factorize this denominator

$q^{2} - 1^{2} = (q - 1) (q + 1)$

here $(q - 1)$ is common between both denominator

So the LCD is $p^{2} (q - 1) (q + 1)$ $p^{2} (q - 1) (q + 1)$

03

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

$\frac{5 q (q + 1)}{p^{2} (q - 1) (q + 1)} + \frac{4 q . p^{2}}{p^{2} (q - 1) (q + 1)}$

04

Step 4.Simplify the numerators.

$\frac{5 q (q + 1)}{p^{2} (q - 1) (q + 1)} + \frac{4 q . p^{2}}{p^{2} (q - 1) (q + 1)}$

05

Step 5. Add numerators of the fractions

$\frac{5 q^{2} + 5 q + 4 p^{2} q}{p^{2} (q - 1) (q + 1)} = \frac{5 q^{2} + 5 q + 4 p^{2} q}{p^{2} (q^{2} - 1)}$

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