Q. 123 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. 123 (page 668)

In the following exercises, perform indicated operations.
$\frac{5 a}{a + 3} - \frac{a + 2}{a + 6}$

Short Answer

Expert verified

The resultant expression is $\begin{array}{rcl} \frac{4 a^{2} + 25 a - 6}{(a + 3) (a + 6)} \end{array}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{5 a}{a + 3} - \frac{a + 2}{a + 6}$ .

Step 2. Express with common denominator

The LCD of the terms of obtained expression is $(a + 3) (a + 6)$ .
Multiply the numerator and denominator of first term by $(a + 6)$ and second term by $(a + 3)$ .

role="math" localid="1645511038690" $\begin{array}{rcl} \frac{5 a (a + 6)}{(a + 3) (a + 6)} - \frac{(a + 2) (a + 3)}{(a + 6) (a + 3)} & = & \frac{5 a^{2} + 30 a}{(a + 3) (a + 6)} - \frac{a^{2} + 2 a + 3 a + 6}{(a + 6) (a + 3)} \\ = & \frac{5 a^{2} + 30 a}{(a + 3) (a + 6)} - \frac{a^{2} + 5 a + 6}{(a + 6) (a + 3)} \end{array}$

Step 3. Simplify

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

$\begin{array}{rcl} \frac{5 a^{2} + 30 a - a^{2} - 5 a - 6}{(a + 3) (a + 6)} \end{array} = \begin{array}{rcl} \frac{4 a^{2} + 25 a - 6}{(a + 3) (a + 6)} \end{array}$

So, the resultant expression is $\begin{array}{rcl} \frac{4 a^{2} + 25 a - 6}{(a + 3) (a + 6)} \end{array}$ .

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91影视

In the following exercises, perform indicated operations.
$\frac{5 a}{a + 3} - \frac{a + 2}{a + 6}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

One App. One Place for Learning.

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91影视

In the following exercises, perform indicated operations. 5aa+3-a+2a+6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{5 a}{a + 3} - \frac{a + 2}{a + 6}$