化简 (x^4+1/(x^4))*(x-1/x)

解答

化简

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

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

求解步骤

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

合并

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

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

使用分式法则:

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

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

化简

(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}}

使用分式法则:

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

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

化简

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

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

e x p an d \frac{2 x ^{3} - x ^{2} + 1}{x ( x - 1 ) ( x + 1 )}

e x p an d \frac{( - 1 ) ^{n} x ^{n + 2}}{3 ^{n + 1} ( n + 2 )}

s im pl i f y (x + 3) (x - \frac{5}{2})

e x p an d \frac{9 ( x ^{2} - 3 )}{x ^{3}}

e x p an d \frac{( 8 s - 16 )}{s ( s + 1 ) ( s ^{2} + 1 )}