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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 56. (page 918)

In the following exercises, simplify.
$\frac{v^{3} + 125}{v^{2} - 25}$

Short Answer

Expert verified

The result is $\frac{v^{2} - 5 v + 25}{v - 5}$ .

Step by step solution

01

Step 1. Given information.

Consider the given rational expression.

$\frac{v^{3} + 125}{v^{2} - 25}$

02

Step 2. Calculation.

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

$\begin{array}{l} \frac{v^{3} + 125}{v^{2} - 25} = \frac{v^{3} + 5^{3}}{v^{2} - 5^{2}} \\ = \frac{(v + 5) (v^{2} - 5 v + 25)}{(v - 5) (v + 5)} \\ = \frac{v^{2} - 5 v + 25}{v - 5} \end{array}$

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