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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. 188 (page 681)

In the following exercises, simplify each complex rational expression using either method.
$\frac{\frac{v}{w} + \frac{1}{v}}{\frac{1}{v} - \frac{v}{w}}$ .

Short Answer

Expert verified

The simplified form is $\frac{v^{2} + w}{w - v^{2}}$ .

Step by step solution

01

Step 1. Given.

The given complex rational expression is: $\frac{\frac{v}{w} + \frac{1}{v}}{\frac{1}{v} - \frac{v}{w}}$ .

02

Step 2. To find

We have to simplify each complex rational expression by using either method.

03

Step 3. Calculation

LCM of the denominators is = $v w$ . Multiply numerator and denominator by it to simplify.

$\frac{\frac{v}{w} + \frac{1}{v}}{\frac{1}{v} - \frac{v}{w}} = \frac{\frac{v}{w} (v w) + \frac{1}{v} (v w)}{\frac{1}{v} (v w) - \frac{v}{w} (v w)} = \frac{v (v) + 1 (w)}{1 (w) - v (v)} = \frac{v^{2} + w}{w - v^{2}}$

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Most popular questions from this chapter

In the following exercise, perform the indicated operation:

$\frac{3 d}{d + 2} + \frac{4}{d} - \frac{d + 8}{d^{2} + 2 d}$

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For the following exercises, perform the indicated operations.

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$f (x) = \frac{4 x}{x^{2} - 3 x - 10} a n d g (x) = \frac{x^{2} - 25}{8 x^{2}}$

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