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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. 92 (page 667)

In the following exercises, add or subtract.
$\frac{20 w}{5 w - 2} + \frac{5 w + 6}{2 - 5 w}$

Short Answer

Expert verified

The sum of the given expressions is 3.

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{20 w}{5 w - 2} + \frac{5 w + 6}{2 - 5 w}$ .

02

Step 2. Multiply the second term by -1-1

Multiply the numerator and denominator of the second term by $- 1$ .

$\frac{20 w}{5 w - 2} + \frac{5 w + 6}{2 - 5 w} = \frac{20 w}{5 w - 2} + \frac{- 5 w - 6}{5 w - 2}$

03

Step 3. Add the numerators

As the denominator is same for both the terms, add the numerator and place over the common denominator.
Add the like terms of the numerator.

$\begin{array}{rcl} \frac{20 w}{5 w - 2} + \frac{- 5 w - 6}{5 w - 2} & = & \frac{20 w - 5 w - 6}{5 w - 2} \\ = & \frac{15 w - 6}{5 w - 2} \end{array}$

04

Step 4. Simplify

Factor the expression in the numerator and then cancel out the common terms in numerator and denominator.

$\begin{array}{rcl} \frac{15 w - 6}{5 w - 2} & = & \frac{3 (5 w - 2)}{5 w - 2} \\ = & 3 \end{array}$

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