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

The solution to a((b(e^{bt}-1))/t-be^{bt} 1/t+e^{bt} 1/(t^2)-1/(t^2)) is a(-b/t+(e^{bt}-1)/(t^2))

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

simplify

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}})

Solution steps

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}})

Simplify

\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})

a^{4} + 13 a^{2} + 40

\frac{3 π}{8} + \frac{π}{8}

t^{2} + t - 30

- 26 x yz + 52 x^{2} y z^{2}

2 x^{4} - x^{3} + 17 x^{2} - 9 x - 9

What is a((b(e^{bt}-1))/t-be^{bt} 1/t+e^{bt} 1/(t^2)-1/(t^2)) ?
The solution to a((b(e^{bt}-1))/t-be^{bt} 1/t+e^{bt} 1/(t^2)-1/(t^2)) is a(-b/t+(e^{bt}-1)/(t^2))