Chapter 8: Q. 8.5 (page 907)

Evaluate $\frac{x^{2} + 1}{x^{2} - 3 x + 2}$ for each value:
$ⓐ x = 0 ⓑ x = - 1 ⓒ x = 3$

Short Answer

Expert verified

$ⓐ The value of \frac{x^{2} + 1}{x^{2} - 3 x + 2} for x = 0 is \frac{1}{2} . ⓑ The value of \frac{x^{2} + 1}{x^{2} - 3 x + 2} for x = - 1 is \frac{1}{3} . ⓒ The value of \frac{x^{2} + 1}{x^{2} - 3 x + 2} for x = 3 is 5 .$

Step by step solution

Step 1. Given Information

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

$ⓐ x = 0 ⓑ x = - 1 ⓒ x = 3$

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} - 3 x + 2} = \frac{{(0)}^{2} + 1}{{(0)}^{2} - 3 \times 0 + 2} \frac{x^{2} + 1}{x^{2} - 3 x + 2} = \frac{0 + 1}{0 - 0 + 2} \frac{x^{2} + 1}{x^{2} - 3 x + 2} = \frac{1}{2}

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} - 3 x + 2} = \frac{{(- 1)}^{2} + 1}{{(- 1)}^{2} - 3 \times (- 1) + 2} \frac{x^{2} + 1}{x^{2} - 3 x + 2} = \frac{1 + 1}{1 + 3 + 2} \frac{x^{2} + 1}{x^{2} - 3 x + 2} = \frac{2}{6} \frac{x^{2} + 1}{x^{2} - 3 x + 2} = \frac{1}{3}

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

Putting $x = 3$ on the given expression

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

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Evaluate $\frac{x^{2} + 1}{x^{2} - 3 x + 2}$ for each value:
$ⓐ x = 0 ⓑ x = - 1 ⓒ x = 3$

Short Answer

Step by step solution

Step 1. Given Information

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

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

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

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Evaluate x2+1x2−3x+2for each value:ⓐx=0ⓑx=−1ⓒx=3

Short Answer

Step by step solution

Step 1. Given Information

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

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Evaluate $\frac{x^{2} + 1}{x^{2} - 3 x + 2}$ for each value:
$ⓐ x = 0 ⓑ x = - 1 ⓒ x = 3$