What is expand (-(ke^{-rt})/r+C)e^{rt} ?

The solution to expand (-(ke^{-rt})/r+C)e^{rt} is -k/r+e^{rt}C

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expand (-(ke^{-rt})/r+C)e^{rt}

expand

(- \frac{k e ^{- r t}}{r} + C) e^{r t}

- \frac{k}{r} + e^{r t} C

Solution steps

(- \frac{k e ^{- r t}}{r} + C) e^{r t}

= e^{r t} (- \frac{k e ^{- r t}}{r} + C)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{r t}, b = - \frac{k e ^{- r t}}{r}, c = C

= e^{r t} (- \frac{k e ^{- r t}}{r}) + e^{r t} C

Apply minus-plus rules

+ (- a) = - a

= - e^{r t} \frac{k e ^{- r t}}{r} + e^{r t} C

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

= - \frac{k}{r} + e^{r t} C

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\frac{4}{( x - 2 ) ( x + 5 )}

(x y^{2} + 2 y cos (x)) d x - (x^{2} y + 2 sin (x)) d y

\frac{( x ^{2} + 3 ) ^{3}}{3}

What is expand (-(ke^{-rt})/r+C)e^{rt} ?
The solution to expand (-(ke^{-rt})/r+C)e^{rt} is -k/r+e^{rt}C