Chapter 7: Q. 119 (page 668)

In the following exercises, perform indicated operations.
$\frac{3 r}{r^{2} + 7 r + 6} + \frac{9}{r^{2} + 4 r + 3}$

Short Answer

Expert verified

The resultant expression is $\frac{3 (r^{2} + 6 r + 18)}{(r + 6) (r + 1) (r + 3)}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{3 r}{r^{2} + 7 r + 6} + \frac{9}{r^{2} + 4 r + 3}$ .

Step 2. Express with common denominator

Factor the denominators of the given expression.

$\frac{3 r}{(r + 6) (r + 1)} + \frac{9}{(r + 3) (r + 1)}$

The LCD of the terms of obtained expression is $(r + 6) (r + 1) (r + 3)$ .
Multiply the numerator and denominator of first term by $(r + 3)$ and second term by $(r + 6)$ .

role="math" localid="1645431186191" $\frac{3 r (r + 3)}{(r + 6) (r + 1) (r + 3)} + \frac{9 (r + 6)}{(r + 3) (r + 1) (r + 6)} = \frac{3 r^{2} + 9 r}{(r + 6) (r + 1) (r + 3)} + \frac{9 r + 54}{(r + 3) (r + 1) (r + 6)}$

Step 3. Simplify

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

$\frac{3 r^{2} + 9 r + 9 r + 54}{(r + 6) (r + 1) (r + 3)} = \frac{3 r^{2} + 18 r + 54}{(r + 6) (r + 1) (r + 3)}$

Factor the numerator and express it in the lowest terms possible.

$\frac{3 (r^{2} + 6 r + 18)}{(r + 6) (r + 1) (r + 3)}$

So, the resultant expression is $\frac{3 (r^{2} + 6 r + 18)}{(r + 6) (r + 1) (r + 3)}$ .

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In the following exercises, perform indicated operations.
$\frac{3 r}{r^{2} + 7 r + 6} + \frac{9}{r^{2} + 4 r + 3}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

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In the following exercises, perform indicated operations. 3rr2+7r+6+9r2+4r+3

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

Calculus

Mechanics Maths

Applied Mathematics

Decision Maths

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{3 r}{r^{2} + 7 r + 6} + \frac{9}{r^{2} + 4 r + 3}$