What is factor 6x^{-1/2}+5x^{1/2}+x^{3/2} ?

The solution to factor 6x^{-1/2}+5x^{1/2}+x^{3/2} is ((x+2)(x+3))/(x^{1/2)}

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factor 6x^{-1/2}+5x^{1/2}+x^{3/2}

factor

6 x^{- \frac{1}{2}} + 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}

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

Solution steps

6 x^{- \frac{1}{2}} + 5 x^{\frac{1}{2}} + x^{\frac{3}{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}}

= 6 x^{- \frac{1}{2}} + 5 x^{- \frac{1}{2}} x^{2 \cdot \frac{1}{2}} + x^{\frac{3}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (6 + 5 x^{2 \cdot \frac{1}{2}}) + x^{\frac{3}{2}}

Apply exponent rule:

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

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

= 6 x^{- \frac{1}{2}} + 5 x^{1} x^{- \frac{1}{2}} + x^{2} x^{- \frac{1}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (6 + 5 x + x^{2})

Factor

x^{2} + 5 x + 6 : (x + 2) (x + 3)

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

Refine

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

- 24 \leq 2 x - 10 < - 6

7 n - 3 = 2 n + 12

\frac{4}{7} \cdot \frac{47}{65} + \frac{10}{7}

2 x - 9 = 1

- 343

What is factor 6x^{-1/2}+5x^{1/2}+x^{3/2} ?
The solution to factor 6x^{-1/2}+5x^{1/2}+x^{3/2} is ((x+2)(x+3))/(x^{1/2)}