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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. 15 (page 917)

In the following exercises, evaluate the rational expression for the given values.
$\frac{m^{2} - 4 n^{2}}{5 m n^{3}} (a) m = 2, n = 1 (b) m = - 1, n = - 1 (c) m = 3, n = 2$

Short Answer

Expert verified

The required answers are

$Part (a) 0 Part (b) - \frac{3}{5} Part (c) - \frac{7}{120}$

Step by step solution

01

Part(a) Step 1. Given Information

The given expression is $\frac{m^{2} - 4 n^{2}}{5 m n^{3}}$

02

Part (a) Step 2. Calculation

Substitute $m = 2, n = 1$ in the given expression,

$\frac{m^{2} - 4 n^{2}}{5 m n^{3}} = \frac{{(2)}^{2} - 4 {(1)}^{2}}{5 (2) {(1)}^{3}} = \frac{4 - 4}{10} = \frac{0}{10} = 0$

03

Part (b) Step 1. Calculation

Substitute $m = - 1, n = - 1$ in the given expression,

$\frac{m^{2} - 4 n^{2}}{5 m n^{3}} = \frac{{(- 1)}^{2} - 4 {(- 1)}^{2}}{5 (- 1) {(- 1)}^{3}} = \frac{1 - 4}{5 (- 1) (- 1)} = \frac{- 3}{5}$

04

Part (c) Step 1. Calculation

Substitute $m = 3, n = 2$ in the given expression,

$\frac{m^{2} - 4 n^{2}}{5 m n^{3}} = \frac{{(3)}^{2} - 4 {(2)}^{2}}{5 (3) {(2)}^{3}} = \frac{9 - 16}{15 (8)} = \frac{- 7}{120}$

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