combinatorics - solving power series expression?

Can anyone show how to simplify $$\frac{\sum_{n=1}^\infty n\frac{n^{n-1}}{n!}x^{n-1}}{(-1+\sum_{n=1}^\infty \frac{n^{n-1}}{n!}x^n)^2}$$

Answer

small hint

the derivative of $$\frac{1}{1-f}$$ is

$$\frac{f'}{(-1+f)^2}.$$