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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{r t}} (C + \frac{k e ^{r t}}{r})

Multiply fractions:

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

= \frac{1 \cdot ( \frac{k e ^{r t}}{r} + C )}{e ^{r t}}

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

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

Join

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

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

Apply the fraction rule:

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

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

(e^{- 1})^{e^{- 1}}

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

(e^{x^{4}})^{2}

28491 \cdot e^{- 0.015 \cdot 380}

\frac{2 ^{π + 1}}{2 ^{π - 1}}

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