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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 404 (page 1069)

In the following exercises, perform the indicated operations.
$\frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25}$

Short Answer

Expert verified

The expression is simplified as $\frac{t + 7}{t - 5}$

Step by step solution

01

Step 1. Given information

Expression:

$\frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25}$

here denominator in both fraction is same.

02

Step 2. Subtract the numerator of both fractions by keeping the denominator same.

$\frac{(5 t^{2} + 4 t + 3) - (4 t^{2} - 8 t - 32)}{t^{2} - 25} = \frac{5 t^{2} + 4 t + 3 - 4 t^{2} + 8 t + 32}{t^{2} - 25} = \frac{t^{2} + 12 t + 35}{t^{2} - 25}$

03

Step 3. Factorize numerator and denominator

$\frac{t^{2} + 7 t + 5 t + 35}{t^{2} - 5^{2}} = \frac{t (t + 7) + 5 (t + 7)}{(t - 5) (t + 5)} = \frac{(t + 5) (t + 7)}{(t - 5) (t + 5)}$

04

Step 4. Cancel common factor in numerator and denominator

$\frac{t + 7}{t - 5}$

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Most popular questions from this chapter

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