What is x^2*(1/(2x^{1/2)}+1) ?

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

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simplify x^2*(1/(2x^{1/2)}+1)

simplify

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

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

Solution steps

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

Join

\frac{1}{2 x ^{\frac{1}{2}}} + 1 : \frac{2 x ^{\frac{1}{2}} + 1}{2 x ^{\frac{1}{2}}}

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

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Simplify

\frac{x ^{2}}{x ^{\frac{1}{2}}} : x^{\frac{3}{2}}

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

δ, x i y y_{2} y_{3} (y_{4} - π)

\frac{3 s - 33}{( s ^{2} + 9 ) ( s + 2 ) ( s - 1 )}

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

sin (2) (x + h)

sin (3) (x^{2} + 1)

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