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coasterface9000
coasterface9000 coasterface9000
  • 31-07-2016
  • Mathematics
Answered

How do I factor (x^2+4)^3/2 - x^2(x^2+4)^-1/2 ?

Verified Answer :

caylus
caylus caylus
  • 31-07-2016

Hello,

\((x^2+4)^{3/2} - x^2(x^2+4)^{-1/2}\\\\ =(x^2+4) \sqrt{x^2+4} - \dfrac{x^2}{\sqrt{x^2+4}} \\\\ =\dfrac{1}{\sqrt{x^2+4}}((x^2+4)^2-x^2)\\\\ =\dfrac{(x^2-x+4)(x^2+x+4)}{\sqrt{x^2+4}}\\\\\)

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