展开 (2sqrt(t)(t-2))/(e^{sqrt(t))t}

解答

展开

\frac{2 t ( t - 2 )}{e ^{t} t}

\frac{2 t}{e ^{t}} - \frac{4}{e ^{t} t}

求解步骤

\frac{2 t ( t - 2 )}{e ^{t} t}

乘开

2 t (t - 2) : 2 t t - 4 t

= \frac{2 t t - 4 t}{e ^{t} t}

使用分式法则:

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

\frac{2 t t - 4 t}{e ^{t} t} = \frac{2 t t}{e ^{t} t} - \frac{4 t}{e ^{t} t}

= \frac{2 t t}{e ^{t} t} - \frac{4 t}{e ^{t} t}

消掉

\frac{2 t t}{e ^{t} t} : \frac{2 t}{e ^{t}}

= \frac{2 t}{e ^{t}} - \frac{4 t}{e ^{t} t}

消掉

\frac{4 t}{e ^{t} t} : \frac{4}{e ^{t} t}

= \frac{2 t}{e ^{t}} - \frac{4}{e ^{t} t}

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