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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. 14 (page 917)

In the following exercises, evaluate the rational expression for the given values.
$\frac{c^{2} + c d - 2 d^{2}}{c d^{3}} (a) c = 2, d = - 1 (b) c = 1, d = - 1 (c) c = - 1, d = 2$

Short Answer

Expert verified

The required answers are

$Part (a) 0 Part (b) 2 Part (c) \frac{9}{8}$

Step by step solution

01

Part(a) Step 1. Given Information

The given expression is $\frac{c^{2} + c d - 2 d^{2}}{c d^{3}}$

02

Part (a) Step 2. Calculation

Substitute $c = 2, d = - 1$ in the given expression,

$\frac{c^{2} + c d - 2 d^{2}}{c d^{3}} = \frac{{(2)}^{2} + (2) (- 1) - 2 {(- 1)}^{2}}{(2) {(- 1)}^{3}} = \frac{4 - 2 - 2}{- 2} = \frac{0}{- 2} = 0$

03

Part (b) Step 1. Calculation

Substitute $c = 1, d = - 1$ in the given expression,

$\frac{c^{2} + c d - 2 d^{2}}{c d^{3}} = \frac{{(1)}^{2} + (1) (- 1) - 2 {(- 1)}^{2}}{(1) {(- 1)}^{3}} = \frac{1 - 1 - 2}{- 1} = \frac{- 2}{- 1} = 2$

04

Part (c) Step 1. Calculation

Substitute $c = - 1, d = 2$ in the given expression,

$\frac{c^{2} + c d - 2 d^{2}}{c d^{3}} = \frac{{(- 1)}^{2} + (- 1) (2) - 2 {(2)}^{2}}{(- 1) {(2)}^{3}} = \frac{1 - 2 - 8}{- 8} = \frac{- 9}{- 8} = \frac{9}{8}$

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