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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 229 (page 954)

Simplify $\frac{5 a}{a - 2} + \frac{9}{a} - \frac{2 a + 18}{a^{2} - 2 a}$ .

Short Answer

Expert verified

The result is $\frac{5 a^{2} + 7 a - 36}{a (a - 2)}$ .

Step by step solution

01

Given Information

The Given expression is $\frac{5 a}{a - 2} + \frac{9}{a} - \frac{2 a + 18}{a^{2} - 2 a}$ .

02

Find the LCD of denominators.

Factor the denominators.

$a^{2} - 2 a = a (a - 2)$

LCD $= a (a - 2)$

Rewrite the expression in factored form.

$= \frac{5 a}{a - 2} + \frac{9}{a} - \frac{2 a + 18}{a (a - 2)}$

03

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{5 a^{2}}{a (a - 2)} + \frac{9 (a - 2)}{a (a - 2)} - \frac{2 a + 18}{a (a - 2)} = \frac{5 a^{2}}{a (a - 2)} + \frac{9 a - 18}{a (a - 2)} - \frac{2 a + 18}{a (a - 2)}$

04

Simplify.

Take common denominator.

$= \frac{5 a^{2} + 9 a - 18 - (2 a + 18)}{a (a - 2)} = \frac{5 a^{2} + 9 a - 18 - 2 a - 18}{a (a - 2)} = \frac{5 a^{2} + 7 a - 36}{a (a - 2)}$

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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, simplify.

$\frac{5 b + 5}{6 b + 6}$

Simplify

In the following exercises, use either method.

$\frac{\frac{2}{r - 9}}{\frac{1}{r + 9} + \frac{3}{r^{2} - 81}}$ .

In the following exercises, simplify.

$\frac{b^{2} + 9 b + 18}{b^{2} - 36}$

. 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?

See all solutions

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