<PRE><B>Question 30271</B>
a^2+2a+1/3 divided by a^2-1/a
= (a^2+2a+1)/3 divided by (a^2-1)/a
= [(a+1)^2/3] divided by [(a+1)(a-1)/a]   
(Using formula a^2 +2ab +b^2 = (a+b)^2 and here a=a and b=1
and formula m^2-n^2 = (m+n)(m-n) where m= a and n= 1)
= [(a+1)^2/3] multiplied  by [a/(a+1)(a-1)]   
= [(a+1)^2 X a]/[3(a+1)(a-1)]  (multplying nr by nr and dr by dr)
=a(a+1)/3(a-1)  (cacelling (a+1) ) 
Answer: a^2+2a+1/3 divided by a^2-1/a
=a(a+1)/3(a-1)  

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