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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 144 (page 940)

Add $\frac{7 x^{2}}{x^{2} - 9} + \frac{21 x}{x^{2} - 9}$

Short Answer

Expert verified

The required expression is $\frac{7 x}{x - 3}$

Step by step solution

01

Given information

The given expression is $\frac{7 x^{2}}{x^{2} - 9} + \frac{21 x}{x^{2} - 9}$

02

Simplifying the expression

The two rational expressions to be added have same denominators, combining the terms:

$\frac{7 x^{2} + 21 x}{x^{2} - 9}$

Factorizing the numerator and denominator:

$\frac{7 x (x + 3)}{(x - 3) (x + 3)}$

Cancelling the common terms from numerator and denominator:

$\frac{7 x}{x - 3}$

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Most popular questions from this chapter

In the following exercises, simplify.

$\frac{56}{63}$

In the following exercises, simplify.

$\frac{\frac{5}{b^{2} - 6 b - 27}}{\frac{3}{b + 3} + \frac{1}{b - 9}}$

When traveling to Great Britain, Bethany exchanged her $900 into 570 British pounds. How many pounds did she receive for each American dollar?

Solve Proportions

$\frac{n + 10}{4} = \frac{40 - n}{6}$

Simplify

In the following exercises, use either method.

$\frac{\frac{v}{w} + \frac{1}{v}}{\frac{1}{v} - \frac{v}{w}}$

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