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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. 16 (page 917)

In the following exercises, evaluate the rational expression for the given values.
$\frac{2 s^{2} t}{s^{2} - 9 t^{2}} (a) s = 4, t = 1 (b) s = - 1, t = - 1 (c) s = 0, t = 2$

Short Answer

Expert verified

The required answers are

$Part (a) \frac{32}{7} Part (b) \frac{1}{4} Part (c) 0$

Step by step solution

01

Part(a) Step 1. Given Information

The given expression is $\frac{2 s^{2} t}{s^{2} - 9 t^{2}}$

02

Part (a) Step 2. Calculation

Substitute $s = 4, t = 1$ in the given expression,

$\frac{2 s^{2} t}{s^{2} - 9 t^{2}} = \frac{2 {(4)}^{2} (1)}{{(4)}^{2} - 9 {(1)}^{2}} = \frac{32}{16 - 9} = \frac{32}{7}$

03

Part (b) Step 1. Calculation

Substitute $s = - 1, t = - 1$ in the given expression,

$\frac{2 s^{2} t}{s^{2} - 9 t^{2}} = \frac{2 {(- 1)}^{2} (- 1)}{{(- 1)}^{2} - 9 {(- 1)}^{2}} = \frac{- 2}{1 - 9} = \frac{- 2}{- 8} = \frac{1}{4}$

04

Part (c) Step 1. Calculation

Substitute $s = 0, t = 2$ in the given expression,

$\frac{2 s^{2} t}{s^{2} - 9 t^{2}} = \frac{2 {(0)}^{2} (2)}{{(0)}^{2} - 9 {(2)}^{2}} = \frac{0}{0 - 36} = 0$

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