What is factor 12x^{-1/2}+7x^{1/2}+x^{3/2} ?

The solution to factor 12x^{-1/2}+7x^{1/2}+x^{3/2} is ((x+3)(x+4))/(x^{1/2)}

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factor 12x^{-1/2}+7x^{1/2}+x^{3/2}

factor

12 x^{- \frac{1}{2}} + 7 x^{\frac{1}{2}} + x^{\frac{3}{2}}

\frac{( x + 3 ) ( x + 4 )}{x ^{\frac{1}{2}}}

Solution steps

12 x^{- \frac{1}{2}} + 7 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}}

= 12 x^{- \frac{1}{2}} + 7 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}} (12 + 7 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}}

= 12 x^{- \frac{1}{2}} + 7 x^{1} x^{- \frac{1}{2}} + x^{2} x^{- \frac{1}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (12 + 7 x + x^{2})

Factor

x^{2} + 7 x + 12 : (x + 3) (x + 4)

= x^{- \frac{1}{2}} (x + 3) (x + 4)

Refine

= \frac{( x + 3 ) ( x + 4 )}{x ^{\frac{1}{2}}}

\frac{b}{8} + \frac{b + 3}{6} \geq - 3

lo g_{5} (4) + lo g_{5} (3)

350000 \cdot \frac{1}{( 1 + 0.1 ) ^{20}}

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

7 - 2 x < 9

What is factor 12x^{-1/2}+7x^{1/2}+x^{3/2} ?
The solution to factor 12x^{-1/2}+7x^{1/2}+x^{3/2} is ((x+3)(x+4))/(x^{1/2)}