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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. 88 (page 1069)

In the following exercises, subtract.
$\frac{5 q^{2} + 3 q - 9}{q^{2} + 6 q + 8} - \frac{4 q^{2} + 9 q + 7}{q^{2} + 6 q + 8}$

Short Answer

Expert verified

The resultant expression is $\frac{q - 8}{q + 4}$ .

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{5 q^{2} + 3 q - 9}{q^{2} + 6 q + 8} - \frac{4 q^{2} + 9 q + 7}{q^{2} + 6 q + 8}$ .

02

Step 2. Subtract the numerator

As the denominator is the same for both the terms, subtract the numerator and place it over the common denominator.

$\begin{array}{rcl} \frac{5 q^{2} + 3 q - 9}{q^{2} + 6 q + 8} - \frac{4 q^{2} + 9 q + 7}{q^{2} + 6 q + 8} & = & \frac{5 q^{2} + 3 q - 9 - 4 q^{2} - 9 q - 7}{q^{2} + 6 q + 8} \\ = & \frac{q^{2} - 6 q - 16}{q^{2} + 6 q + 8} \end{array}$

03

Step 3. Factor the expression

Factor the expression in the numerator and denominator, and then cancel out the common terms from the numerator and denominator.

$\frac{(q + 2) (q - 8)}{(q + 4) (q + 2)} = \frac{q - 8}{q + 4}$

So, the resultant expression is $\frac{q - 8}{q + 4}$ .

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Most popular questions from this chapter

Solve $25 p^{2} = 49$ $25 p^{2} = 49$

Simplify:

(a) ${(- 256)}^{\frac{1}{4}}$

(b) ${- 256}^{\frac{1}{4}}$

(c) ${(256)}^{- \frac{1}{4}}$

In the following exercises, add the polynomials.

$(x^{2} + 6 x + 8) + (- 4 x^{2} + 11 x - 9)$

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$\frac{1}{2} - \frac{4}{x^{2}} 鈮� \frac{1}{x}$

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