Answer
$R=\frac{Ir}{1-I}$.
Work Step by Step
Multiply both sides of the given equation by $(R+r)$ to clear fractions.
$(R+r)\cdot I=(R+r)\cdot \frac{R}{(R+r)}$
Use the distributive property and cancel the common terms.
$IR+Ir=R$
Add $-IR$ to each side of the equation.
$IR+Ir-IR=R-IR$
Simplify.
$Ir=R-IR$
Factor out $R$.
$Ir=R(1-I)$
Divide both sides by $(1-I)$.
$\frac{Ir}{(1-I)}=\frac{R(1-I)}{(1-I)}$
Cancel the common terms.
$R=\frac{Ir}{1-I}$.
