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Math
Elementary Algebra
Chapter 8
546 - Review Exercises

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: 546 - Review Exercises (page 1025)

Subtract Rational Expressions with a Common Denominator
In the following exercises, subtract.
$\frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25} .$

Short Answer

Expert verified

The answer is $\frac{t + 7}{t - 5} .$

Step by step solution

01

Step 1. Given Information.

Given:

$\frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25}$ having the same denominator.

02

Step 2. Solving the given expression.

$A s t h e d e n o m i n a t o r i s s a m e s o w e c a n d i r e c t l y s u b t r a c t t h e n u m e r a t o r s : \frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25} = \frac{5 t^{2} + 4 t + 3 - (4 t^{2} - 8 t - 32)}{t^{2} - 25} = \frac{5 t^{2} + 4 t + 3 - 4 t^{2} + 8 t + 32}{t^{2} - 25} = \frac{t^{2} + 12 t + 35}{t^{2} - 25} = \frac{(t + 5) (t + 7)}{(t + 5) (t - 5)} = \frac{t + 7}{t - 5} .$

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