Chapter 8: 545 - Review Exercises (page 1025)

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

Short Answer

Expert verified

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

Step by step solution

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.

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

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solving the given expression.

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Subtract Rational Expressions with a Common DenominatorIn the following exercises, subtract.4q2-q+3q2+6q+5-3q2+q+6q2+6q+5.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solving the given expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Mechanics Maths

Calculus

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

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