SOLUTION: Can you help me divide the rational expression. a^2+2a+1/3 divided by a^2-1/a

Question 30271: Can you help me divide the rational expression.
a^2+2a+1/3 divided by a^2-1/a

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
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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