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^{- \frac{1}{2}} x^{2 \cdot \frac{1}{2}}

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

Factor out common term

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

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

(62 + 2 X) (54 + 2 X)

12 = - 8 b

\frac{( - 10 ) - 7}{( - 10 ) ^{2} - 49}

\frac{3 5}{2 2}

lo g_{7} (9) + lo g_{7} (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)}