Improper Integral of a Rational Function

Evaluate: $$\int_0^\infty \frac{1}{\left(x+\frac{1}{x}\right)^2}\ \mathrm{d}x$$The answer is in the form $\frac{\alpha \pi}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.