What is factor x^{3/2}-x^{1/2}-6x^{-1/2} ?

The solution to factor x^{3/2}-x^{1/2}-6x^{-1/2} is ((x+2)(x-3))/(x^{1/2)}

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factor x^{3/2}-x^{1/2}-6x^{-1/2}

factor

x^{\frac{3}{2}} - x^{\frac{1}{2}} - 6 x^{- \frac{1}{2}}

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

Solution steps

x^{\frac{3}{2}} - x^{\frac{1}{2}} - 6 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}} - x^{- \frac{1}{2}} x^{2 \cdot \frac{1}{2}} - 6 x^{- \frac{1}{2}}

Factor out common term

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

= x^{\frac{3}{2}} - x^{- \frac{1}{2}} (x^{2 \cdot \frac{1}{2}} + 6)

Apply exponent rule:

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

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

= x^{2} x^{- \frac{1}{2}} - x^{1} x^{- \frac{1}{2}} - 6 x^{- \frac{1}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (x^{2} - x - 6)

Factor

x^{2} - x - 6 : (x + 2) (x - 3)

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

Refine

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

\frac{1}{2} x^{4} - x^{3} - 36 x^{2} + 108 x + 80

\frac{5 - i}{2 + i}

x + \frac{x}{2} = 1 + 2 x

r^{2} + 12 r + 36 = 0

\frac{9 + i}{- 6 - 2 i}

What is factor x^{3/2}-x^{1/2}-6x^{-1/2} ?
The solution to factor x^{3/2}-x^{1/2}-6x^{-1/2} is ((x+2)(x-3))/(x^{1/2)}