Given the following equation shown in the picture:
[tex]\frac{E}{e}=\frac{R+r}{r}[/tex]
You can solve for the variable "e" by following the steps shown below:
Step 1. You must apply the Multiplication property of equality by multiplying both sides of the equation by "e". As you can see below:
[tex]\begin{gathered} (e)(\frac{E}{e})=(e)(\frac{R+r}{r}) \\ \\ E=\frac{e(R+r)}{r} \end{gathered}[/tex]
Step 2. Now you must apply the Multiplication property of equality again by multiplying both sides of the equation by "r":
[tex]\begin{gathered} (r)(E)=(r)(\frac{e(R+r)}{r}) \\ \\ Er=(1)e(R+r) \\ Er=e(R+r) \end{gathered}[/tex]
Step 3. Finally, apply the Division property of equality by dividing both sides of the equation by:
[tex](R+r)[/tex]
Then, you get:
[tex]\begin{gathered} \frac{Er}{(R+r)}=\frac{e(R+r)}{(R+r)} \\ \\ \frac{Er}{R+r}=e \end{gathered}[/tex]
Therefore, the answer is:
[tex]e=\frac{Er}{R+r}[/tex]
