What is x^{3/2}*(sqrt(x)-1/(sqrt(x))) ?

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

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simplify x^{3/2}*(sqrt(x)-1/(sqrt(x)))

simplify

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

x (x - 1)

Solution steps

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

Join

x - \frac{1}{x} : \frac{x - 1}{x}

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

Apply the fraction rule:

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

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

Simplify

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

= x (x - 1)

x^{2} + x y - 20 y^{2}

5 x^{2} + 9 x = - 4

x^{2} - 7 x - 30

53 \cdot \frac{π}{180}

2 x^{2} y + 2 x z^{2} + y^{2} z^{2} + x y^{3}

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