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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.35 (page 661)

Add:
$\frac{1}{m^{2} - m - 2} + \frac{5 m}{m^{2} + 3 m + 2}$

Short Answer

Expert verified

The required sum is $\begin{array}{rcl} \frac{5 m^{2} - 9 m + 2}{(m + 1) (m - 2) (m + 2)} \end{array}$ .

Step by step solution

01

Step 1. Given information

The given expression is $\frac{1}{m^{2} - m - 2} + \frac{5 m}{m^{2} + 3 m + 2}$

02

Step 2. Find LCD

Factor the denominators of both the rational expressions.

$m^{2} - m - 2 = (m + 1) (m - 2) m^{2} + 3 m + 2 = (m + 2) (m + 1)$

So, the LCD is $(m + 1) (m - 2) (m + 2)$ .

03

Step 3. Express the expression with LCD

Rewrite each rational expression in terms of LCD.

$\frac{1}{m^{2} - m - 2} = \frac{m + 2}{(m + 1) (m - 2) (m + 2)} \frac{5 m}{m^{2} + 3 m + 2} = \frac{5 m^{2} - 10 m}{(m + 1) (m - 2) (m + 2)}$

04

Step 4. Add the obtained Expressions

Add the expressions with LCD.

$\begin{array}{rcl} \frac{m + 2}{(m + 1) (m - 2) (m + 2)} + \frac{5 m^{2} - 10 m}{(m + 1) (m - 2) (m + 2)} & = & \frac{m + 2 + 5 m^{2} - 10 m}{(m + 1) (m - 2) (m + 2)} \\ = & \frac{5 m^{2} - 9 m + 2}{(m + 1) (m - 2) (m + 2)} \end{array}$

So, the required sum is $\begin{array}{rcl} \frac{5 m^{2} - 9 m + 2}{(m + 1) (m - 2) (m + 2)} \end{array}$

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Most popular questions from this chapter

Simplify the complex rational expression by writing it as division:

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