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

Step 1. Given information.

The following expression is given:

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

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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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

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:2qq+5+3q-3-13q+15q2+2q-15

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

Logic and Functions

Probability and Statistics

Statistics

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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