Exponential and Logarithmic Functions · Superchallenge problem

Let $f(x)=\ln\!\left(\dfrac{1+x}{1-x}\right)$ for $-1<x<1$. Find the number $c$ with $-1<c<1$ such that $f(c)=f\!\left(\tfrac12\right)+f\!\left(\tfrac13\right)$.