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Chapter 7: Q. 417 (page 736)

In the following exercises, perform the indicated operations

3yy+2-y+2y+8

Short Answer

Expert verified

Simplified expression is2y2+20y-4(y+2)(y+8)

Step by step solution

01

Step 1. Given Information  

Expression:

3yy+2-y+2y+8
02

Step 2. Find LCD 

Denominator of first fraction is y+2

Denominator of the second fraction is y+8

here nothing is common between both denominator

So the LCD is y+2y+8

03

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

3y(y+8)(y+2)(y+8)-(y+2)(y+2)(y+2)(y+8)

04

Step 4.Simplify the numerators.

3y2+24y(y+2)(y+8)-(y+2)2(y+2)(y+8)=3y2+24y(y+2)(y+8)-y2+4y+4(y+2)(y+8)

05

Step 5. Subtract numerators

3y2+24y-(y2+4y+4)(y+2)(y+8)

06

Step 6. Simplify numerator

3y2+24y-y2-4y-4(y+2)(y+8)=2y2+20y-4(y+2)(y+8)

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