Geometry Challenge – 3 ⭐⭐⭐

A fixed point $Q$ lies on the bisector of $\angle{P}$. A moving point $A$ lies on one side of $\angle{P}$, with line $AQ$ intersecting the other side of $\angle{P}$ at point $B$. Show that $\dfrac{1}{PA}+\dfrac{1}{PB}$ is a constant.