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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q141E. (page 668)

In the following exercise, perform the indicated operation:
$\frac{3 d}{d + 2} + \frac{4}{d} - \frac{d + 8}{d^{2} + 2 d}$

Short Answer

Expert verified

$\frac{3 (d + 1)}{(d + 2)}$

Step by step solution

01

Step 1. Given information.

The following expression is given:

$\frac{3 d}{d + 2} + \frac{4}{d} - \frac{d + 8}{d^{2} + 2 d}$

02

Step 2. Perform the indicated operation.

Factorise the denominators:

$\frac{3 d}{d + 2} + \frac{4}{d} - \frac{d + 8}{d (d + 2)}$

Find out the LCD:

$d (d + 2)$

Rewrite the expression with denominators equal to the LCD:

$\frac{3 d . d}{d (d + 2)} + \frac{4 (d + 2)}{d (d + 2)} - \frac{d + 8}{d (d + 2)}$

Simplify:

$\frac{3 d^{2} + 4 d + 8 - d - 8}{d (d + 2)} \frac{3 d^{2} + 3 d}{d (d + 2)} \frac{3 d (d + 1)}{d (d + 2)}$

Cancel the common factors:

$\frac{3 (d + 1)}{(d + 2)}$

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Most popular questions from this chapter

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$\frac{2 y^{2} - 10 y z - 48 z^{2}}{2 y - 1} 梅 (4 y^{2} - 32 y z)$

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$\frac{v - 5}{11 - v} 梅 \frac{v^{2} - 25}{v - 11}$

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