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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. 17 (page 651)

Simplify the rational expression $\frac{8 b^{2} - 32}{2 b^{2} - 6 b - 80}$

Short Answer

Expert verified

Simplified form of rational expression $\frac{8 b^{2} - 32 b}{2 b^{2} - 6 b - 80} i s \frac{4 b (b - 4)}{(b + 5) (b - 8)} w h e r e b 鈮� - 5, 8$

Step by step solution

01

. Given information

Given rational expression is $\frac{8 b^{2} - 32 b}{2 b^{2} - 6 b - 80} .$

Simplify the given rational expression.

02

. Simplification of rational expression

For the simplification factor both numerator and denominator separately , divide out the common factor and then simplify.

Hence simplified for of the given expression is

$\frac{8 b^{2} - 32 b}{2 b^{2} - 6 b - 80} = \frac{8 b (b - 4)}{2 (b^{2} - 3 b - 40)} = \frac{8 b (b - 4)}{2 (b + 5) (b - 8)} = \frac{4 b (b - 4)}{(b + 5) (b - 8)} w h e r e b 鈮� - 5, 8, 4$

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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 exercises, find the domain of each function.

$R (x) = \frac{3 x^{2} + 15 x}{6 x^{2} + 6 x - 36}$

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

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

Simplify the complex rational expression by using the LCD:

$\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$

In the following exercises, divide the rational expressions.

$\frac{3 s^{2}}{s^{2} - 16} 梅 \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}$

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