What is (x^2+1/(x^2))(x-1/x) ?

The solution to (x^2+1/(x^2))(x-1/x) is ((x^4+1)(x^2-1))/(x^3)

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simplify (x^2+1/(x^2))(x-1/x)

simplify

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

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

Solution steps

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

Join

x^{2} + \frac{1}{x ^{2}} : \frac{x ^{4} + 1}{x ^{2}}

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

x x^{2} : x^{3}

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

\frac{\frac{d}{d x} ( 5 x )}{( ( 5 - 3 x ) ^{3} )}

8 (\frac{3}{2} + 3 u)

(3 - \frac{3}{2} y) (3 - \frac{3}{2} y)

(4 + e^{- 2 t})^{2}

\frac{( k _{2} y + h _{2} x + 1 ) ^{2}}{k _{2} + h _{2}}

What is (x^2+1/(x^2))(x-1/x) ?
The solution to (x^2+1/(x^2))(x-1/x) is ((x^4+1)(x^2-1))/(x^3)