Chapter 7: Q. 414 (page 736)

In the following exercises, perform the indicated operations
$\frac{3 x}{x^{2} - 9} + \frac{5}{x^{2} + 6 x + 9}$

Short Answer

Expert verified

The simplified expression is $\frac{3 x^{2} + 14 x - 15}{{(x + 3)}^{2} (x - 3)}$

Step by step solution

Step 1. Given information

Expression :

\frac{3 x}{x^{2} - 9} + \frac{5}{x^{2} + 6 x + 9}

Step 2. Find LCD

Denominator of first fraction is $x^{2} - 9$

Factorize this denominator

$x^{2} - 3^{2} = (x - 3) (x + 3)$

Denominator of the second fraction is $x^{2} + 6 x + 9$

Factorize this denominator

$x^{2} + 2.3 . x + 3^{2} = {(x + 3)}^{2}$

here $(x + 3)$ is common between both denominator

So the LCD is ${(x + 3)}^{2} (x - 3)$

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

$\frac{3 x (x + 3)}{{(x + 3)}^{2} (x - 3)} + \frac{5 (x - 3)}{{(x + 3)}^{2} (x - 3)}$

Step 4.Simplify the numerators.

$\frac{3 x^{2} + 9 x}{{(x + 3)}^{2} (x - 3)} + \frac{5 x - 15}{{(x + 3)}^{2} (x - 3)}$

Step 5. Add numerators of the fractions

$\frac{3 x^{2} + 9 x + 5 x - 15}{{(x + 3)}^{2} (x - 3)}$

Step 6. Simplify numerator

$\frac{3 x^{2} + 14 x - 15}{{(x + 3)}^{2} (x - 3)}$

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In the following exercises, perform the indicated operations
$\frac{3 x}{x^{2} - 9} + \frac{5}{x^{2} + 6 x + 9}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find LCD

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

Step 4.Simplify the numerators.

Step 5. Add numerators of the fractions

Step 6. Simplify numerator

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In the following exercises, perform the indicated operations 3xx2-9+5x2+6x+9

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find LCD

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

Step 4.Simplify the numerators.

Step 5. Add numerators of the fractions

Step 6. Simplify numerator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations
$\frac{3 x}{x^{2} - 9} + \frac{5}{x^{2} + 6 x + 9}$