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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 36. (page 918)

In the following exercises, simplify.
$\frac{v^{2} + 8 v + 15}{v^{2} - v - 12}$

Short Answer

Expert verified

The result is $\frac{v + 5}{v - 4}$ .

Step by step solution

01

Step 1. Given information.

Consider the given rational expression.

$\frac{v^{2} + 8 v + 15}{v^{2} - v - 12}$

02

Step 2. Calculation.

Factor the numerator and denominator and remove the common factor from the numerator and the denominator.

$\begin{array}{l} \frac{v^{2} + 8 v + 15}{v^{2} - v - 12} = \frac{v^{2} + 5 v + 3 v + 15}{v^{2} - 4 v + 3 v - 12} \\ = \frac{v (v + 5) + 3 (v + 5)}{v (v - 4) + 3 (v - 4)} \\ = \frac{(v + 5) (v + 3)}{(v - 4) (v + 3)} \end{array} = \frac{v + 5}{v - 4}$

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