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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. 9 (page 917)

In the following exercises, evaluate the rational expression for the given values.
$\frac{y^{2} + 5 y + 6}{y^{2} - 1} (a) y = 0 (b) y = 2 (c) y = - 2$

Short Answer

Expert verified

The required answers are

$Part (a) - 6 Part (b) \frac{20}{3} Part (c) 0$

Step by step solution

01

Part(a) Step 1. Given Information

The given expression is $\frac{y^{2} + 5 y + 6}{y^{2} - 1}$

02

Part (a) Step 2. Calculation

Substitute 0 for y,

$\frac{y^{2} + 5 y + 6}{y^{2} - 1} = \frac{{(0)}^{2} + 5 (0) + 6}{{(0)}^{2} - 1} = \frac{6}{- 1} = - 6$

03

Part (b) Step 1. Calculation

Substitute 2 for y,

$\frac{y^{2} + 5 y + 6}{y^{2} - 1} = \frac{{(2)}^{2} + 5 (2) + 6}{{(2)}^{2} - 1} = \frac{4 + 10 + 6}{4 - 1} = \frac{20}{3}$

04

Part (c) Step 1. Calculation

Substitute $- 2$ for y,

$\frac{y^{2} + 5 y + 6}{y^{2} - 1} = \frac{{(- 2)}^{2} + 5 (- 2) + 6}{{(- 2)}^{2} - 1} = \frac{4 - 10 + 6}{4 - 1} = \frac{0}{3} = 0$

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