展开 ((1+a^2)(1+b^2))/(ab)

解答

展开

\frac{( 1 + a ^{2} ) ( 1 + b ^{2} )}{ab}

\frac{1}{ab} + \frac{b}{a} + \frac{a}{b} + ab

求解步骤

\frac{( 1 + a ^{2} ) ( 1 + b ^{2} )}{ab}

乘开

(1 + a^{2}) (1 + b^{2}) : 1 + b^{2} + a^{2} + a^{2} b^{2}

= \frac{1 + b ^{2} + a ^{2} + a ^{2} b ^{2}}{ab}

使用分式法则:

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

\frac{1 + b ^{2} + a ^{2} + a ^{2} b ^{2}}{ab} = \frac{1}{ab} + \frac{b ^{2}}{ab} + \frac{a ^{2}}{ab} + \frac{a ^{2} b ^{2}}{ab}

= \frac{1}{ab} + \frac{b ^{2}}{ab} + \frac{a ^{2}}{ab} + \frac{a ^{2} b ^{2}}{ab}

消掉

\frac{b ^{2}}{ab} : \frac{b}{a}

= \frac{1}{ab} + \frac{b}{a} + \frac{a ^{2}}{ab} + \frac{a ^{2} b ^{2}}{ab}

消掉

\frac{a ^{2}}{ab} : \frac{a}{b}

= \frac{1}{ab} + \frac{b}{a} + \frac{a}{b} + \frac{a ^{2} b ^{2}}{ab}

消掉

\frac{a ^{2} b ^{2}}{ab} : ab

= \frac{1}{ab} + \frac{b}{a} + \frac{a}{b} + ab

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

e x p an d 4 (2 sin (x - 2 t) + 2 e^{x + 2 t})

e x p an d \frac{( ( x + 1 ) ( x + 2 ) ( 2 x + 3 ) )}{6}

e x p an d \frac{6 x - 42}{( x - 4 ) ( x - 6 )}

e x p an d cos (π (0.5 + h))