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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. 7.13 (page 646)

Simplify $\frac{x^{3} - 8}{3 x^{2} - 6 x + 12} 梅 \frac{x^{2} - 4}{6}$

Short Answer

Expert verified

The simplest form of the given expression is

$\frac{2 (x^{2} + 2 x + 4)}{3 (x^{2} - 2 x + 4) (x + 2)} .$

Step by step solution

01

Step 1. Given information

The given expression is $\frac{x^{3} - 8}{3 x^{2} - 6 x + 12} 梅 \frac{x^{2} - 4}{6} .$

02

Step 2. Simplify

$\frac{x^{3} - 8}{3 x^{2} - 6 x + 12} 梅 \frac{x^{2} - 4}{6} = \frac{x^{3} - 8}{3 x^{2} - 6 x + 12} 脳 \frac{6}{x^{2} - 4} Convertdivisionintomultiplication = \frac{(x - 2) (x^{2} + 2 x + 4)}{3 (x^{2} - 2 x + 4)} 脳 \frac{6}{(x - 2) (x + 2)} Factorizenumeratoranddenominator = \frac{2 (x^{2} + 2 x + 4)}{3 (x^{2} - 2 x + 4) (x + 2)} Removecommonfactorsofnumeratoranddenominator$

Hence, the simplified expression is $\frac{2 (x^{2} + 2 x + 4)}{3 (x^{2} - 2 x + 4) (x + 2)} .$

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Most popular questions from this chapter

In the following exercise, perform the indicated operation:

$\frac{6 d}{d - 5} + \frac{1}{d + 4} - \frac{7 d - 5}{d^{2} - d - 20}$

In the following exercise, find

(a) $R (x) = f (x) + g (x)$

(b) $R (x) = f (x) - g (x)$ :

$f (x) = \frac{- 5 x - 5}{x^{2} + x - 6} g (x) = \frac{x + 1}{2 - x}$

Determine the values for which the rational expression is undefined.

$\frac{5 a + 3}{3 a - 2}$

Simplify the complex rational expression by writing it as a division:

$\frac{\frac{1}{2} + \frac{2}{3}}{\frac{5}{6} + \frac{1}{12}}$

Divide $\frac{y^{2} - 16}{4} 梅 \frac{y^{3} - 64}{2 y^{2} + 8 y + 32}$

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