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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q137E. (page 668)

In the following expression, perform the indicated operation:
$\frac{5 a}{a - 2} + \frac{9}{a} - \frac{2 a + 18}{a^{2} - 2 a}$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

The following expression is given:

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

02

Step 2. Perform the indicated operation.

Factor the denominator and numerator (where applicable):

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

Find the LCD:

$a (a - 2)$

Rewrite the expression with LCD at the denominator:

role="math" localid="1644731961868" $\frac{5 a^{2}}{a (a - 2)} + \frac{9 (a - 2)}{a (a - 2)} - \frac{2 a + 18}{a (a - 2)}$

Simplify:

role="math" localid="1644732100403" $\frac{5 a^{2} + 9 a - 18 - 2 a - 18}{a (a - 2)} \frac{5 a^{2} + 7 a - 36}{a (a - 2)}$

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Most popular questions from this chapter

In the following exercise, perform the indicated operation:

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