# How do you solve for e in E/e=(R+r)/r?

Mar 16, 2017

$e = \frac{r E}{R + r}$

#### Explanation:

Given:$\text{ } \frac{E}{e} = \frac{R + r}{r}$

Using first principles:

$\textcolor{b l u e}{\text{YOU CAN DO THIS:"->"Turn everything upside down giving:}}$

$\textcolor{g r e e n}{\frac{e}{E} = \frac{r}{R + r}}$

Multiply both sides by E

$\textcolor{g r e e n}{\frac{e}{E} \textcolor{red}{\times E} \text{ "=" } \frac{r}{R + r} \textcolor{red}{\times E}}$

color(green)(e xx(color(red)(E))/E" "=" "(rE)/(R+r)

But $\frac{E}{E} = 1$ and $1 \times e = e$

$e = \frac{r E}{R + r}$