What is factor x^{-5/2}+2x^{-3/2}+x^{-1/2} ?

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

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factor x^{-5/2}+2x^{-3/2}+x^{-1/2}

factor

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

\frac{( x + 1 ) ^{2}}{x ^{\frac{5}{2}}}

Solution steps

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

Apply exponent rule:

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

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

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

Factor out common term

x^{- \frac{5}{2}}

= x^{- \frac{5}{2}} (1 + 2 x + x^{2})

Factor

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

= x^{- \frac{5}{2}} (x + 1)^{2}

Refine

= \frac{( x + 1 ) ^{2}}{x ^{\frac{5}{2}}}

\frac{24}{6}

2 x^{3} - 3 x^{2} - 7 x + 10

\frac{2 ^{- 4}}{4 ^{0}}

y - 22 = - 144

\frac{7}{6} (6 d - 18) - 23 = 19

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