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91Ó°ÊÓ

In the following exercises, perform the indicated operations

5qp2q-p2+4qq2-1

Short Answer

Expert verified

Simplified expression is 5q2+5q+4p2qp2(q2-1)

Step by step solution

01

Step 1. Given expression   

5qp2q-p2+4qq2-1

02

Step 2. Find LCD    

Denominator of first fraction is p2q-p2

Factorize this denominator

p2(q-1)

Denominator of the second fraction isq2-1

Factorize this denominator

q2-12=(q-1)(q+!)

here (q-1)is common between both denominator

So the LCD isp2(q-1)(q+1)

03

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

5q(q+1)p2(q-1)(q+1)+4q.p2p2(q-1)(q+1)

04

Step 4.Simplify the numerators.     

5q2+5qp2(q-1)(q+1)+4p2qp2(q-1)(q+1)

05

Step 5. Add numerators of the fractions  

5q2+5q+4p2qp2(q-1)(q+1)=5q2+5q+4p2qp2(q2-1)

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