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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q142E. (page 668)

In the following exercise, perform the indicated operation:
$\frac{2 q}{q + 5} + \frac{3}{q - 3} - \frac{13 q + 15}{q^{2} + 2 q - 15}$

Short Answer

Expert verified

$\frac{2 q (q - 8)}{(q + 5) (q - 3)}$

Step by step solution

01

Step 1. Given information.

The following expression is given:

$\frac{2 q}{q + 5} + \frac{3}{q - 3} - \frac{13 q + 15}{q^{2} + 2 q - 15}$

02

Step 2. Perform the indicated operation.

Factorise the denominators:

$\frac{2 q}{q + 5} + \frac{3}{q - 3} - \frac{13 q + 15}{(q + 5) (q - 3)}$

Find out the LCD:

$(q + 5) (q - 3)$

Rewrite the expression with the denominators equal to the LCD:

$\frac{2 q (q - 3)}{(q + 5) (q - 3)} + \frac{3 (q + 5)}{(q + 5) (q - 3)} - \frac{13 q + 15}{(q + 5) (q - 3)}$

Simplify:

$\frac{2 q^{2} - 6 q + 3 q + 15 - 13 q - 15}{(q + 5) (q - 3)} \frac{2 q^{2} - 16 q}{(q + 5) (q - 3)} \frac{2 q (q - 8)}{(q + 5) (q - 3)}$

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