化简 a((b(e^{bt}-1))/t-be^{bt} 1/t+e^{bt} 1/(t^2)-1/(t^2))

解答

化简

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

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

求解步骤

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

b e^{b t} \frac{1}{t} = \frac{e ^{b t} b}{t}

e^{b t} \frac{1}{t ^{2}} = \frac{e ^{b t}}{t ^{2}}

= a (\frac{e ^{b t}}{t ^{2}} + \frac{b ( e ^{b t} - 1 )}{t} - \frac{e ^{b t} b}{t} - \frac{1}{t ^{2}})

化简

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

= a (\frac{e ^{b t} - 1}{t ^{2}} + \frac{b ( e ^{b t} - 1 ) - e ^{b t} b}{t})

\frac{b ( e ^{b t} - 1 ) - b e ^{b t}}{t} = - \frac{b}{t}

= a (\frac{e ^{b t} - 1}{t ^{2}} - \frac{b}{t})

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