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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. 42 (page 652)

In the following exercises, multiply the rational expressions.
$\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} . \frac{n^{2} - 10 n + 25}{2 n^{2} - 13 n + 21}$

Short Answer

Expert verified

The simplified rational expression is $\frac{- (n + 2) (n - 5)}{(n + 5) (n - 3)}$

Step by step solution

01

Step 1. Given Information

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

We have to multiply the given rational expression.

02

Step 2. Factor the numerators and denominators

$= \frac{(2 n - 7) (n + 2)}{(5 + n) (5 - n)} . \frac{(n - 5) (n - 5)}{(2 n - 7) (n - 3)} = \frac{(2 n - 7) (n + 2) (n - 5) (n - 5)}{- (5 + n) (n - 5) (2 n - 7) (n - 3)}$

03

Step 3. Remove the common factors and simplify

$= \frac{- (n + 2) (n - 5)}{(n + 5) (n - 3)}$

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Most popular questions from this chapter

The distance a moving body travels, $d$ , varies directly with the time, $t$ , it moves. The train travels 100 miles in 2 hours.

Write the equation that relates $d a n d t$ .
How many miles would it travel in 5 hours?

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

In the following exercise, perform the indicated operation:

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

Write the steps you would use to explain solving rational inequalities to your little brother.

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

$R (x) = \frac{x^{3} - 2 x^{2} - 25 x + 50}{x^{2} - 25}$

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