What is (x^4+1/(x^4))*(x-1/x) ?

The solution to (x^4+1/(x^4))*(x-1/x) is ((x^8+1)(x^2-1))/(x^5)

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simplify (x^4+1/(x^4))*(x-1/x)

simplify

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

\frac{( x ^{8} + 1 ) ( x ^{2} - 1 )}{x ^{5}}

Solution steps

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

Join

x^{4} + \frac{1}{x ^{4}} : \frac{x ^{8} + 1}{x ^{4}}

= \frac{x ^{8} + 1}{x ^{4}} (x - \frac{1}{x})

Apply the fraction rule:

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

= \frac{( x ^{8} + 1 ) ( x - \frac{1}{x} )}{x ^{4}}

Simplify

(x^{8} + 1) (x - \frac{1}{x}) : \frac{( x ^{8} + 1 ) ( x ^{2} - 1 )}{x}

= \frac{\frac{( x ^{8} + 1 ) ( x ^{2} - 1 )}{x}}{x ^{4}}

Apply the fraction rule:

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

= \frac{( x ^{8} + 1 ) ( x ^{2} - 1 )}{x x ^{4}}

Simplify

x x^{4} : x^{5}

= \frac{( x ^{8} + 1 ) ( x ^{2} - 1 )}{x ^{5}}

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

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

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

\frac{9 ( x ^{2} - 3 )}{x ^{3}}

\frac{( 8 s - 16 )}{s ( s + 1 ) ( s ^{2} + 1 )}

What is (x^4+1/(x^4))*(x-1/x) ?
The solution to (x^4+1/(x^4))*(x-1/x) is ((x^8+1)(x^2-1))/(x^5)