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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 39. (page 918)

In the following exercises, simplify.
$\frac{y^{2} - 2 y - 3}{y^{2} - 9}$

Short Answer

Expert verified

The result is $\frac{y + 1}{y + 3}$ .

Step by step solution

01

Step 1. Given information.

Consider the given rational expression.

$\frac{y^{2} - 2 y - 3}{y^{2} - 9}$

02

Step 2. Calculation.

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

$\begin{array}{l} \frac{y^{2} - 2 y - 3}{y^{2} - 9} = \frac{y^{2} - 3 y + y - 3}{y^{2} - 3^{2}} \\ = \frac{y (y - 3) + (y - 3)}{(y + 3) (y - 3)} \\ = \frac{(y + 1) (y - 3)}{(y + 3) (y - 3)} \\ = \frac{y + 1}{y + 3} \end{array}$

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