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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. 8.5 (page 907)

Evaluate $\frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2}$ for each value:
$鈸� x = 0 鈸� x = 鈭� 1 鈸� x = 3$

Short Answer

Expert verified

$鈸� The value of \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} for x = 0 is \frac{1}{2} . 鈸� The value of \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} for x = - 1 is \frac{1}{3} . 鈸� The value of \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} for x = 3 is 5 .$

Step by step solution

01

Step 1. Given Information

Evaluate $\frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2}$ for each value:

$鈸� x = 0 鈸� x = 鈭� 1 鈸� x = 3$

02

Part (a) Step 1. Finding the value of x2+1x2−3x+2 for x=0

Putting $x = 0$ on the given expression

\frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{{(0)}^{2} + 1}{{(0)}^{2} 鈭� 3 脳 0 + 2} \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{0 + 1}{0 鈭� 0 + 2} \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{1}{2}

03

Part (b) Step 1. Finding the value of x2+1x2−3x+2 for x=-1.

Putting $x = - 1$ on the given expression

\frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{{(- 1)}^{2} + 1}{{(- 1)}^{2} 鈭� 3 脳 (- 1) + 2} \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{1 + 1}{1 + 3 + 2} \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{2}{6} \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{1}{3}

04

Part (c) Step 1. Finding the value of x2+1x2−3x+2 for x=3

Putting $x = 3$ on the given expression

localid="1648640957993" $\frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{{(3)}^{2} + 1}{{(3)}^{2} 鈭� 3 脳 3 + 2} \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{9 + 1}{9 鈭� 9 + 2} \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = \frac{10}{2} \frac{x^{2} + 1}{x^{2} 鈭� 3 x + 2} = 5$

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