What is factor 3x^{3/2}-9x^{1/2}+6x^{-1/2} ?

The solution to factor 3x^{3/2}-9x^{1/2}+6x^{-1/2} is 3(x^{3/2}-3x^{1/2}+2*1/(x^{1/2)})

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factor 3x^{3/2}-9x^{1/2}+6x^{-1/2}

factor

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} + 6 x^{- \frac{1}{2}}

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

Solution steps

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} + 6 x^{- \frac{1}{2}}

Factor out common term

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

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

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

- 8 \leq 4 x - 2 < 0

\frac{x ^{2} - 3 x - 4}{x ^{2} + 6 x + 5} < 0

\frac{x - 9}{2} < - 10

5 x^{2} - 39 x - 8 = 0

\frac{2}{3} + 3

What is factor 3x^{3/2}-9x^{1/2}+6x^{-1/2} ?
The solution to factor 3x^{3/2}-9x^{1/2}+6x^{-1/2} is 3(x^{3/2}-3x^{1/2}+2*1/(x^{1/2)})