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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 8.86 (page 947)

Add: $\frac{7}{2 m + 6} + \frac{4}{m^{2} + 4 m + 3}$

Short Answer

Expert verified

The Simplification of the expression is $\frac{7 m + 15}{2 (m + 1) (m + 3)}$ .

Step by step solution

01

Given information

The given rational expression is $\frac{7}{2 m + 6} + \frac{4}{m^{2} + 4 m + 3}$

02

The simplification of the rational expression

$\frac{7}{2 m + 6} + \frac{4}{m^{2} + 4 m + 3}$

Factor the denominator

$\frac{7}{2 m + 6} + \frac{4}{m^{2} + 3 m + 1 m + 3} \frac{7}{2 (m + 3)} + \frac{4}{m (m + 3) + (m + 3)} \frac{7}{2 (m + 3)} + \frac{4}{(m + 1) (m + 3)}$

The LCD of the expression is $2 (m + 1) (m + 3)$ .

$\frac{7 (m + 1)}{2 (m + 3) (m + 1)} + \frac{4 脳 2}{2 (m + 1) (m + 3)}$

Simplify the numerator

$\frac{7 m + 7}{2 (m + 3) (m + 1)} + \frac{8}{2 (m + 1) (m + 3)} \frac{7 m + 15}{2 (m + 1) (m + 3)}$

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