What is expand-(v(e^{-kt}-1))/k ?

The solution to expand-(v(e^{-kt}-1))/k is -(e^{-kt}v)/k+v/k

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expand-(v(e^{-kt}-1))/k

expand

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

- \frac{e ^{- k t} v}{k} + \frac{v}{k}

Solution steps

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

Expand

v (e^{- k t} - 1) : e^{- k t} v - v

= - \frac{e ^{- k t} v - v}{k}

Apply the fraction rule:

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

\frac{e ^{- k t} v - v}{k} = - (\frac{e ^{- k t} v}{k}) - (- \frac{v}{k})

= - (\frac{e ^{- k t} v}{k}) - (- \frac{v}{k})

Remove parentheses:

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

= - \frac{e ^{- k t} v}{k} + \frac{v}{k}

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What is expand-(v(e^{-kt}-1))/k ?
The solution to expand-(v(e^{-kt}-1))/k is -(e^{-kt}v)/k+v/k