展开-(V(e^{-at}-1))/a

解答

展开

- \frac{V ( e ^{- a t} - 1 )}{a}

- \frac{e ^{- a t} V}{a} + \frac{V}{a}

求解步骤

- \frac{V ( e ^{- a t} - 1 )}{a}

乘开

V (e^{- a t} - 1) : e^{- a t} V - V

= - \frac{e ^{- a t} V - V}{a}

使用分式法则:

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

\frac{e ^{- a t} V - V}{a} = - (\frac{e ^{- a t} V}{a}) - (- \frac{V}{a})

= - (\frac{e ^{- a t} V}{a}) - (- \frac{V}{a})

去除括号:

(a) = a, - (- a) = a

= - \frac{e ^{- a t} V}{a} + \frac{V}{a}

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