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}

(x + 3) (x - 5 + 5 i) (x + 5 + 5 i)

\frac{1}{4} (5 + 2 x) (3 - 2 x)

\frac{( 107 s + 302 )}{12 ( s ^{2} - 2 s + 12 )}

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

(x + 1) (x + 1)