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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. 277 (page 966)

In the following exercises, simplify:
$\frac{\frac{1}{p} + \frac{1}{q}}{\frac{1}{p^{2}} - \frac{1}{q^{2}}}$ .

Short Answer

Expert verified

The simplified rational expression is, $\frac{p q}{q - p}$ .

Step by step solution

01

Step 1. Given Information.

The rational expression is,

$\frac{\frac{1}{p} + \frac{1}{q}}{\frac{1}{p^{2}} - \frac{1}{q^{2}}}$ .

02

Step 2. Simplifying the rational expression.

$\frac{\frac{1}{p} + \frac{1}{q}}{\frac{1}{p^{2}} - \frac{1}{q^{2}}}$

The LCD of the expression is $p^{2} q^{2}$ ,

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

Using $(a^{2} - b^{2}) = (a + b) (a - b)$ in the denominator,

role="math" localid="1647791789739" $= \frac{p q (q + p)}{(q + p) (q - p)}$

Removing common factors,

role="math" localid="1647791863927" $= \frac{p q}{q - p}$ .

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