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Math
Elementary Algebra
Ch 8
545 - Review Exercises

545 - Review Exercises

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Elementary Algebra

Found in: Page 1025

Book edition 2nd

Author(s) Lynn Marecek, MaryAnne Anthony-Smith

Pages 1240 pages

ISBN 9780998625713

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Short Answer

Subtract Rational Expressions with a Common Denominator
In the following exercises, subtract.
$\frac{4 q^{2} - q + 3}{q^{2} + 6 q + 5} - \frac{3 q^{2} + q + 6}{q^{2} + 6 q + 5} .$

The answer is $\frac{q - 3}{q + 5} .$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given:

$\frac{4 q^{2} - q + 3}{q^{2} + 6 q + 5} - \frac{3 q^{2} + q + 6}{q^{2} + 6 q + 5}$ having same denominator.

Step 2. Solving the given expression.

$A s t h e d e n o m i n a t o r i s s a m e s o w e c a n d i r e c t l y s u b t r a c t t h e n u m e r a t o r s : \frac{4 q^{2} - q + 3}{q^{2} + 6 q + 5} - \frac{3 q^{2} + q + 6}{q^{2} + 6 q + 5} = \frac{4 q^{2} - q + 3 - (3 q^{2} + q + 6)}{q^{2} + 6 q + 5} = \frac{4 q^{2} - q + 3 - 3 q^{2} - q - 6}{q^{2} + 6 q + 5} = \frac{q^{2} - 2 q - 3}{q^{2} + 6 q + 5} = \frac{(q + 1) (q - 3)}{(q + 1) (q + 5)} = \frac{q - 3}{q + 5} .$

Most popular questions for Math Textbooks

Simplify

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In the following exercises, simplify:

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