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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. 264 (page 966)

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

Short Answer

Expert verified

The simplified form of the given expression is $\frac{q + p^{2}}{q^{2} - p}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

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

02

Step 2. Concept.

The following concept is required for simplification:

$\frac{A}{B} 梅 \frac{C}{D} = \frac{A}{B} 路 \frac{D}{C}$

03

Step 3. Rewrite the expression and then simplify.

Simplify the numerator and denominator.

$= \frac{\frac{q + p^{2}}{p q}}{\frac{q^{2} - p}{p q}} = \frac{q + p^{2}}{p q} 梅 \frac{q^{2} - p}{p q}$

Rewrite as the product of first times the reciprocal of the second.

$= \frac{q + p^{2}}{p q} 路 \frac{p q}{q^{2} - p} = \frac{q + p^{2}}{q^{2} - p}$

04

Step 4. Conclusion.

The simplified form of the given expression is $\frac{q + p^{2}}{q^{2} - p}$ .

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