What is factor x^{-7/2}+2x^{-5/2}+x^{-3/2} ?

The solution to factor x^{-7/2}+2x^{-5/2}+x^{-3/2} is ((x+1)^2)/(x^{7/2)}

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factor x^{-7/2}+2x^{-5/2}+x^{-3/2}

factor

x^{- \frac{7}{2}} + 2 x^{- \frac{5}{2}} + x^{- \frac{3}{2}}

\frac{( x + 1 ) ^{2}}{x ^{\frac{7}{2}}}

Solution steps

x^{- \frac{7}{2}} + 2 x^{- \frac{5}{2}} + x^{- \frac{3}{2}}

Apply exponent rule:

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

x^{- \frac{5}{2}} = x^{1 +- \frac{7}{2}} = x^{1} x^{- \frac{7}{2}}, x^{- \frac{3}{2}} = x^{2 +- \frac{7}{2}} = x^{2} x^{- \frac{7}{2}}

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

Factor out common term

x^{- \frac{7}{2}}

= x^{- \frac{7}{2}} (1 + 2 x + x^{2})

Factor

x^{2} + 2 x + 1 : (x + 1)^{2}

= x^{- \frac{7}{2}} (x + 1)^{2}

Refine

= \frac{( x + 1 ) ^{2}}{x ^{\frac{7}{2}}}

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What is factor x^{-7/2}+2x^{-5/2}+x^{-3/2} ?
The solution to factor x^{-7/2}+2x^{-5/2}+x^{-3/2} is ((x+1)^2)/(x^{7/2)}