Let $\displaystyle f(x)=\frac{x^{2}} {1+x^2}$

Compute:

$\displaystyle f(\frac{1}{1}) + f(\frac{1}{2})+...+f(\frac{1}{10}) + f(\frac{2}{1})+f(\frac{2}{2})+...+f(\frac{2}{10})+ f(\frac{3}{1})+f(\frac{3}{2})+...+f(\frac{3}{10})+ ...+f(\frac{10}{1})+f(\frac{10}{2})+...+f(\frac{10 }{10})$

Thanks in advance!