jmc

We have the equation $\frac{3+x}{5+x}=\frac{1+x}{2+x}$. Simplifying, we get $$\begin{array}{rl}(3+x)(2+x)& =(5+x)(1+x)\\ 6+5x+x^2& =5+6x+x^2\\ x& =\boxed{1}.\end{array}$$