What is factor 4x^{-9/2}+4x^{-7/2}+x^{-5/2} ?

The solution to factor 4x^{-9/2}+4x^{-7/2}+x^{-5/2} is ((x+2)^2)/(x^{9/2)}

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factor 4x^{-9/2}+4x^{-7/2}+x^{-5/2}

factor

4 x^{- \frac{9}{2}} + 4 x^{- \frac{7}{2}} + x^{- \frac{5}{2}}

\frac{( x + 2 ) ^{2}}{x ^{\frac{9}{2}}}

Solution steps

4 x^{- \frac{9}{2}} + 4 x^{- \frac{7}{2}} + x^{- \frac{5}{2}}

Factor out common term

4

= 4 (x^{- \frac{9}{2}} + x^{- \frac{7}{2}}) + x^{- \frac{5}{2}}

Factor

x^{- \frac{9}{2}} + x^{- \frac{7}{2}} : \frac{1 + x}{x ^{\frac{9}{2}}}

= x^{- \frac{5}{2}} + 4 \cdot \frac{x + 1}{x ^{\frac{9}{2}}}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{- \frac{7}{2}} = x^{1 +- \frac{9}{2}} = x^{1} x^{- \frac{9}{2}}, x^{- \frac{5}{2}} = x^{2 +- \frac{9}{2}} = x^{2} x^{- \frac{9}{2}}

= 4 x^{- \frac{9}{2}} + 4 x^{1} x^{- \frac{9}{2}} + x^{2} x^{- \frac{9}{2}}

Factor out common term

x^{- \frac{9}{2}}

= x^{- \frac{9}{2}} (4 + 4 x + x^{2})

Factor

x^{2} + 4 x + 4 : (x + 2)^{2}

= x^{- \frac{9}{2}} (x + 2)^{2}

Refine

= \frac{( x + 2 ) ^{2}}{x ^{\frac{9}{2}}}

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What is factor 4x^{-9/2}+4x^{-7/2}+x^{-5/2} ?
The solution to factor 4x^{-9/2}+4x^{-7/2}+x^{-5/2} is ((x+2)^2)/(x^{9/2)}