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

Step 1. Given information.

The following expression is given:

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

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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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

Step by step solution

Step 1. Given information.

Step 2. Perform the indicated operation.

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In the following exercise, perform the indicated operation:3dd+2+4d-d+8d2+2d

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Perform the indicated operation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Decision Maths

Statistics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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