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}}}

- 2 ∣ 3 - 2 x ∣ = - 6

8 x^{2} + 6 x + 1 = 0

12 x^{2} + 69 x + 45

7 (x - 1) = 2 (3 x + 1)

5 - \frac{1}{5}

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)}