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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. 91 (page 667)

In the following exercises, add or subtract.
$\frac{10 v}{2 v - 1} + \frac{2 v + 4}{1 - 2 v}$

Short Answer

Expert verified

The sum of both the expressions is 4.

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{10 v}{2 v - 1} + \frac{2 v + 4}{1 - 2 v}$ .

02

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

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

$\frac{10 v}{2 v - 1} + \frac{2 v + 4}{1 - 2 v} = \frac{10 v}{2 v - 1} + \frac{- 2 v - 4}{2 v - 1}$

03

Step 3. Add the numerators

Step 3. Subtract 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.

$\begin{array}{rcl} \frac{10 v}{2 v - 1} + \frac{- 2 v - 4}{2 v - 1} & = & \frac{10 v - 2 v - 4}{2 v - 1} \\ = & \frac{8 v - 4}{2 v - 1} \end{array}$

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{8 v - 4}{2 v - 1} & = & \frac{4 (2 v - 1)}{2 v - 1} \\ = & 4 \end{array}

The sum is 4.

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Most popular questions from this chapter

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)}$

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.

$f (x) = \frac{2 x^{2} + 8 x}{x^{2} - 9 x + 20} a n d g (x) = \frac{x - 5}{x^{2}}$

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$\frac{\frac{1}{x^{2}} - \frac{1}{y^{2}}}{\frac{1}{x} + \frac{1}{y}}$

Simplify the complex rational expression by using the LCD:

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