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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. 7.10 (page 645)

Simplify $\frac{9 x^{2}}{x^{2} + 11 x + 30} 路 \frac{x^{2} - 36}{3 x^{2}}$ .

Short Answer

Expert verified

The simplest form of the given expression is $\frac{3 (x - 6)}{(x + 5)} .$

Step by step solution

01

Step 1. Given information

The given expression is $\frac{9 x^{2}}{x^{2} + 11 x + 30} 路 \frac{x^{2} - 36}{3 x^{2}} .$

02

Step 2. Simplify

$\frac{9 x^{2}}{x^{2} + 11 x + 30} 路 \frac{x^{2} - 36}{3 x^{2}} = \frac{3 路 3 路 x 路 x}{(x + 5) (x + 6)} 路 \frac{(x - 6) (x + 6)}{3 路 x 路 x} Factorizenumeratoranddenominator = \frac{3 路 3 路 x 路 x (x - 6) (x + 6)}{3 路 x 路 x (x + 5) (x + 6)} Multiply numerator and denominator = \frac{3 (x - 6)}{(x + 5)} Removethecommonfactorsofnumeratoranddenominator$

Hence, the given expression is simplified as $\frac{3 (x - 6)}{(x + 5)} .$

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Most popular questions from this chapter

For the following exercises, perform the indicated operations.

$\frac{6 q + 3}{9 q^{2} - 9 q} 梅 \frac{q^{2} + 14 q + 33}{q^{2} + 4 q - 5} . \frac{4 q^{2} + 12 q}{12 q + 6}$

In the following exercise, perform the indicated operation:

$\frac{2 b}{b - 5} + \frac{3}{2 b} - \frac{2 b - 15}{2 b^{2} - 10 b}$

Simplify the rational expression $\frac{36 v^{3} w^{2}}{27 v w^{3}} .$

Simplify the complex rational expression by using the LCD:

$\frac{\frac{3}{x + 2}}{\frac{5}{x - 2} - \frac{3}{x^{2} - 4}}$

In the following exercises, multiply the rational expressions.

$\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} . \frac{n^{2} - 10 n + 25}{2 n^{2} - 13 n + 21}$

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