Q. 128 In the following exercises, perf... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 128 (page 668)

In the following exercises, perform indicated operations.
$\frac{7 q + 8}{q^{2} - 2 q - 24} - \frac{q + 2}{4 - q}$

Short Answer

Expert verified

The required expression is $\begin{array}{rcl} \frac{- (q^{2} - 9 q - 32)}{(q - 6) (q + 4)} \end{array}$ .

Step by step solution

Step 1. Given information

The given expression is $\frac{7 q + 8}{q^{2} - 2 q - 24} - \frac{q + 2}{4 - q}$ .

Step 2. Find LCD

Factor the denominator of first term.

$q^{2} - 2 q - 24 = (q - 6) (q + 4)$

As the denominators have no common term, the LCD is $(q - 6) (q + 4) (4 - q)$

Step 3. Express with LCD

Express the given expression with LCD as denominators of both the terms.

$\begin{array}{rcl} \frac{7 q + 8}{q^{2} - 2 q - 24} - \frac{q + 2}{4 - q} & = & \frac{(7 q + 8) (4 - q)}{(q - 6) (q + 4) (4 - q)} - \frac{(q + 2) (q - 6) (q + 4)}{(q - 6) (q + 4) (4 - q)} \\ = & \frac{- 7 q^{2} + 20 q + 32}{(q - 6) (q + 4) (4 - q)} - \frac{- q^{3} + 6 q^{2} + 16 q - 96}{(q - 6) (q + 4) (4 - q)} \end{array}$

Step 4. Simplify

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

$\begin{array}{rcl} \frac{- 7 q^{2} + 20 q + 32 + q^{3} - 6 q^{2} - 16 q + 96}{(q - 6) (q + 4) (4 - q)} & = & \frac{q^{3} - 13 q^{2} + 4 q + 128}{(q - 6) (q + 4) (4 - q)} \\ = & \frac{(q - 4) (q^{2} - 9 q - 32)}{(q - 6) (q + 4) (4 - q)} \\ = & \frac{- (q^{2} - 9 q - 32)}{(q - 6) (q + 4)} \end{array}$

So, the required expression is $\begin{array}{rcl} \frac{- (q^{2} - 9 q - 32)}{(q - 6) (q + 4)} \end{array}$ .

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91影视

In the following exercises, perform indicated operations.
$\frac{7 q + 8}{q^{2} - 2 q - 24} - \frac{q + 2}{4 - q}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find LCD

Step 3. Express with LCD

Step 4. Simplify

One App. One Place for Learning.

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91影视

In the following exercises, perform indicated operations.7q+8q2-2q-24-q+24-q

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find LCD

Step 3. Express with LCD

Step 4. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{7 q + 8}{q^{2} - 2 q - 24} - \frac{q + 2}{4 - q}$