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

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

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User LaSombra
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8.3k points

1 Answer

6 votes
Hello,


(x^2+4)^(3/2) - x^2(x^2+4)^(-1/2)\\\\ =(x^2+4) √(x^2+4) - (x^2)/(√(x^2+4)) \\\\ =(1)/(√(x^2+4))((x^2+4)^2-x^2)\\\\ =((x^2-x+4)(x^2+x+4))/(√(x^2+4))\\\\
answered
User Cmo
by
8.4k points
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