What is sqrt(x)(x-1/x) ?

The solution to sqrt(x)(x-1/x) is (x^2-1)/(sqrt(x))

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simplify sqrt(x)(x-1/x)

simplify

x (x - \frac{1}{x})

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

Solution steps

x (x - \frac{1}{x})

Join

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

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

Apply the fraction rule:

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

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

Apply radical rule:

a = a a

x = x x

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

Cancel the common factor:

x

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

(1 + 2 i)^{5}

6 x (3 - 2 x)

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

\frac{x ^{5}}{( x ^{2} + 4 ) ^{2}}

x (1 + x)