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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.7 (page 644)

Simplify $\frac{x^{2} - 4 x - 5}{25 - x^{2}}$

Short Answer

Expert verified

The simplest form of the given expression is $- \frac{(x + 1)}{(x + 5)} .$

Step by step solution

01

Step 1. Given information

The given rational expression is $\frac{x^{2} - 4 x - 5}{25 - x^{2}}$

02

Step 2. Simplify

$\frac{x^{2} - 4 x - 5}{25 - x^{2}} = \frac{(x - 5) (x + 1)}{(5 - x) (5 + x)} Factorizenumeratoranddenominator = - \frac{(x - 5) (x + 1)}{(x - 5) (x + 5)} Rewritetheexpression = - \frac{(x + 1)}{(x + 5)} Removethecommonfactorsofnumeratoranddenominator$

Hence, the simplified expression is $- \frac{(x + 1)}{(x + 5)}$

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Most popular questions from this chapter

For the following exercises, perform the indicated operations.

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

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

Joon drove 4 hours to his home, driving 208 miles on the interstate and 40 miles on the country roads. If he drove 15 mph faster on the interstate than on the country roads, what was his rate on the country roads?

Simplify the complex rational expression by writing it as division:

$\frac{\frac{3}{4} - \frac{1}{3}}{\frac{1}{8} + \frac{5}{6}}$

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?

See all solutions

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