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

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

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factor x^{(-3)/2}+2x^{(-1)/2}+x^{1/2}

factor

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

\frac{( x + 1 ) ^{2}}{x ^{\frac{3}{2}}}

Solution steps

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

Apply exponent rule:

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

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

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

Factor out common term

x^{\frac{- 3}{2}}

= x^{\frac{- 3}{2}} (1 + 2 x + x^{2})

Factor

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

= x^{\frac{- 3}{2}} (x + 1)^{2}

Refine

= \frac{( x + 1 ) ^{2}}{x ^{\frac{3}{2}}}

(x - 2)^{2} = - 5 x - 8

\frac{1}{2} - \frac{3}{2}

36 - 8 x^{2} = 0

- 9 x + 5 < 17

12 x^{2} + 2 x - 4

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