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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. 49 (page 652)

In the following exercises, divide the rational expressions.
$\frac{x^{2} + 3 x - 10}{4 x} 梅 (2 x^{2} + 20 x + 50)$

Short Answer

Expert verified

The simplified rational expression is $\frac{(x - 2)}{8 x (x + 5)} .$

Step by step solution

01

Step 1. Given Information

$\frac{x^{2} + 3 x - 10}{4 x} 梅 (2 x^{2} + 20 x + 50)$

= \frac{x^{2} + 3 x - 10}{4 x} 脳 \frac{1}{2 x^{2} + 20 x + 50}

02

Step 2. Factors the numerator and denominator

$= \frac{(x + 5) (x - 2)}{4 x} 脳 \frac{1}{2 (x + 5) (x + 5)} = \frac{(x + 5) (x - 2)}{2 脳 4 x (x + 5) (x + 5)}$

03

Step 3. Remove the common factors

$= \frac{(x - 2)}{8 x (x + 5)}$

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Most popular questions from this chapter

Divide the rational expression $\frac{3 y^{2} - 12 y - 63}{4 y + 3} 梅 (6 y^{2} - 42 y)$

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

$\frac{\frac{2}{x^{2} - 1}}{\frac{3}{x + 1}}$

In the following exercise, perform the indicated operation:

$\frac{3}{2 x^{2} + 5 x + 2} - \frac{1}{2 x^{2} + 3 x + 1}$

In the following exercises, multiply the rational expressions.

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

In the following exercises, find the domain of each function.

$R (x) = \frac{8 x^{2} - 32 x}{2 x^{2} - 6 x - 80}$

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