化简 (x+1/x)(x-1/x)

解答

化简

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

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

求解步骤

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

合并

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

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

使用分式法则:

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

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

化简

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

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

使用分式法则:

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

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

使用指数法则:

aa = a^{2}

xx = x^{2}

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

e x p an d \frac{d}{d x} ((2 A x + B) e^{x}) + e^{x} (A x^{2} + B x + C)

e x p an d (cos (x) + sin (x))^{4}

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

e x p an d \frac{x ^{4} + 3 x ^{2}}{( x ^{2} + 1 ) ^{2}}

e x p an d sin (x) cos (x) (sec (x) + cot (x))