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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 67. (page 919)

In the following exercises, simplify each rational expression.
$\frac{a^{2} - 5 a - 36}{81 - a^{2}}$

Short Answer

Expert verified

The result is $- \frac{(a + 4)}{(9 + a)}$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\frac{a^{2} - 5 a - 36}{81 - a^{2}}$

02

Step 2. Factor the fraction.

Factor the numerator and denominator of the given fraction and remove common factors.

$\begin{array}{l} \frac{a^{2} - 5 a - 36}{81 - a^{2}} = \frac{a^{2} - 9 a + 4 a - 36}{9^{2} - a^{2}} \\ = \frac{a (a - 9) + 4 (a - 9)}{(9 - a) (9 + a)} \\ = \frac{(a - 9) (a + 4)}{(9 - a) (9 + a)} \\ = \frac{- (9 - a) (a + 4)}{(9 - a) (9 + a)} \\ = - \frac{(a + 4)}{(9 + a)} \end{array}$

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Most popular questions from this chapter

Ironing Lenore can do the ironing for her family鈥檚 business in h hours. Her daughter would take h + 2 hours to get the ironing done. If Lenore and her daughter work together, using 2 irons, the number of hours it would take them to do all the ironing is $\frac{1}{\frac{1}{h} + \frac{1}{h + 2}}$ .

Simplify the complex fraction $\frac{1}{\frac{1}{h} + \frac{1}{h + 2}}$ .
Find the number of hours it would take Lenore and her daughter, working together, to get the ironing done if $h = 4$ .

In the following exercises, solve.

$\frac{7}{9} + \frac{1}{x} = \frac{2}{3}$

In the following exercises, simplify.

$\frac{\frac{1}{2} + \frac{5}{6}}{\frac{2}{3} + \frac{7}{9}}$

. In this section, you learned to simplify the complex fraction $\frac{\frac{3}{x + 2}}{\frac{x}{x^{2} - 4}}$

two ways: rewriting it as a division problem multiplying the numerator and denominator by the LCD Which method do you prefer? Why?

In the following exercises, simplify.

$\frac{v^{2} + 8 v + 15}{v^{2} - v - 12}$

See all solutions

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