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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 8: Q 143 (page 940)

Add $\frac{2 w^{2}}{w^{2} - 16} + \frac{8 w}{w^{2} - 16}$

Short Answer

Expert verified

The required expression is $\frac{2 w}{w - 4}$

Step by step solution

01

Given information

The given expression is $\frac{2 w^{2}}{w^{2} - 16} + \frac{8 w}{w^{2} - 16}$

02

Simplifying the expression

The denominators are same, combining the terms:

$\frac{2 w^{2} + 8 w}{w^{2} - 16}$

Factorizing the numerator and denominator:

$\frac{2 w (w + 4)}{(w - 4) (w + 4)}$

Cancelling the common terms from numerator and denominator:

$\frac{2 w}{(w - 4)}$

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Most popular questions from this chapter

In the following exercises, simplify.

$\frac{\frac{1}{2} + \frac{3}{4}}{\frac{3}{5} + \frac{7}{10}}$

Simplify

In the following exercises, use either method.

$\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}}$ .

In the following exercises, solve.

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Electronics The resistance of a circuit formed by connecting two resistors in parallel is $\frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}}}$ .

Simplify the complex fraction role="math" localid="1647789125778" $\frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}}}$ .
Find the resistance of the circuit when $R_{1} = 8$ and $R_{2} = 12$ .

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In the following exercises, use either method.

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