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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 203 (page 954)

Add $\frac{2 m}{3 m - 3} + \frac{5 m}{m^{2} + 3 m - 4}$ .

Short Answer

Expert verified

The sum is $\frac{2 m^{2} + 23 m}{3 (m - 1) (m + 4)}$ .

Step by step solution

01

Given Information

The Given expression is $\frac{2 m}{3 m - 3} + \frac{5 m}{m^{2} + 3 m - 4}$ .

02

Find the LCD of denominators.

Factor the denominators.

$3 m - 3 = 3 (m - 1)$

$m^{2} + 3 m - 4 = (m - 1) (m + 4)$

LCD $= 3 (m - 1) (m + 4)$ .

Rewrite the expression.

$= \frac{2 m}{3 (m - 1)} + \frac{5 m}{(m - 1) (m + 4)}$

03

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{2 m (m + 4)}{3 (m - 1) (m + 4)} + \frac{5 m (3)}{3 (m - 1) (m + 4)}$

Simplify numerator.

$= \frac{2 m^{2} + 8 m}{3 (m - 1) (m + 4)} + \frac{15 m}{3 (m - 1) (m + 4)}$

04

Add

Take common denominator.

$= \frac{2 m^{2} + 8 m + 15 m}{3 (m - 1) (m + 4)}$

$= \frac{2 m^{2} + 23 m}{3 (m - 1) (m + 4)}$

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