Chapter 7: Q. 421 (page 736)

In the following exercises, perform the indicated operations
$\frac{8 a}{a^{2} - 64} - \frac{4}{a + 8}$

Short Answer

Expert verified

The simplified expression is $\frac{4}{a - 8}$

Step by step solution

Step 1. Given information

Expression:

\frac{8 a}{a^{2} - 64} - \frac{4}{a + 8}

Step 2. Find LCD

Denominator of the first fraction is $a^{2} - 64$

It can be factorize as

$a^{2} - 8^{2} = (a - 8) (a + 8)$

Denominator of the second fraction is $a + 8$

Here $(a + 8)$ is common to the both denominators

So LCD is $(a - 8) (a + 8)$

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

$\frac{8 a}{(a - 8) (a + 8)} - \frac{4 (a - 8)}{(a + 8) (a - 8)}$

Step 4. Simplify numerators

$\frac{8 a}{(a - 8) (a + 8)} - \frac{4 a - 32}{(a + 8) (a - 8)}$

Step 5. Subtract numerators

$\frac{8 a - (4 a - 32)}{(a - 8) (a + 8)} = \frac{8 a - 4 a + 32}{(a - 8) (a + 8)} = \frac{4 a + 32}{(a - 8) (a + 8)}$

Step 6. Take 4 common out of numerator and then cancel common factors

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

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In the following exercises, perform the indicated operations
$\frac{8 a}{a^{2} - 64} - \frac{4}{a + 8}$

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 numerators

Step 5. Subtract numerators

Step 6. Take 4 common out of numerator and then cancel common factors

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In the following exercises, perform the indicated operations 8aa2-64-4a+8

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 numerators

Step 5. Subtract numerators

Step 6. Take 4 common out of numerator and then cancel common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Calculus

Decision Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations
$\frac{8 a}{a^{2} - 64} - \frac{4}{a + 8}$