展开 ((e^{kt}-1)sqrt(k^2+1))/k

解答

展开

\frac{( e ^{k t} - 1 ) k ^{2} + 1}{k}

\frac{e ^{k t} k ^{2} + 1}{k} - \frac{k ^{2} + 1}{k}

求解步骤

\frac{( e ^{k t} - 1 ) k ^{2} + 1}{k}

乘开

(e^{k t} - 1) k^{2} + 1 : e^{k t} k^{2} + 1 - k^{2} + 1

= \frac{e ^{k t} k ^{2} + 1 - k ^{2} + 1}{k}

使用分式法则:

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

\frac{e ^{k t} k ^{2} + 1 - k ^{2} + 1}{k} = \frac{e ^{k t} k ^{2} + 1}{k} - \frac{k ^{2} + 1}{k}

= \frac{e ^{k t} k ^{2} + 1}{k} - \frac{k ^{2} + 1}{k}

e x p an d 6 (e - 3)

e x p an d \frac{9 ( x - 3 )}{( x - 2 ) ( x - 1 )}

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

e x p an d (x - 1)^{2} y^{''} (x) + (x - 1) y^{'} (x) - 4 y

e x p an d (x + 2)^{2}