What is expand (30(-ke^{-kt}t-e^{-kt}))/k ?

The solution to expand (30(-ke^{-kt}t-e^{-kt}))/k is -30e^{-kt}t-(30e^{-kt})/k

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expand (30(-ke^{-kt}t-e^{-kt}))/k

expand

\frac{30 ( - k e ^{- k t} t - e ^{- k t} )}{k}

- 30 e^{- k t} t - \frac{30 e ^{- k t}}{k}

Solution steps

\frac{30 ( - k e ^{- k t} t - e ^{- k t} )}{k}

Expand

30 (- k e^{- k t} t - e^{- k t}) : - 30 k e^{- k t} t - 30 e^{- k t}

= \frac{- 30 k e ^{- k t} t - 30 e ^{- k t}}{k}

Apply the fraction rule:

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

\frac{- 30 k e ^{- k t} t - 30 e ^{- k t}}{k} = - \frac{30 k e ^{- k t} t}{k} - \frac{30 e ^{- k t}}{k}

= - \frac{30 k e ^{- k t} t}{k} - \frac{30 e ^{- k t}}{k}

Cancel

\frac{30 k e ^{- k t} t}{k} : 30 e^{- k t} t

= - 30 e^{- k t} t - \frac{30 e ^{- k t}}{k}

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What is expand (30(-ke^{-kt}t-e^{-kt}))/k ?
The solution to expand (30(-ke^{-kt}t-e^{-kt}))/k is -30e^{-kt}t-(30e^{-kt})/k