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Chapter 7: Q. 421 (page 736)

In the following exercises, perform the indicated operations

8aa2-64-4a+8

Short Answer

Expert verified

The simplified expression is 4a-8

Step by step solution

01

Step 1. Given information

Expression:

8aa2-64-4a+8
02

Step 2. Find LCD      

Denominator of the first fraction isa2-64

It can be factorize as

a2-82=(a-8)(a+8)

Denominator of the second fraction is a+8

Here a+8is common to the both denominators

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

03

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

8a(a-8)(a+8)-4(a-8)(a+8)(a-8)

04

Step 4. Simplify numerators

8a(a-8)(a+8)-4a-32(a+8)(a-8)

05

Step 5. Subtract numerators

8a-(4a-32)(a-8)(a+8)=8a-4a+32(a-8)(a+8)=4a+32(a-8)(a+8)

06

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

4(a+8)(a-8)(a+8)=4a-8

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