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

Step 1. Given Information.

The rational expression is,

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

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 $p^{2} q^{2}$ ,

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

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplifying the rational expression.

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In the following exercises, simplify:1p+1q1p2-1q2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplifying the rational expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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