I have to show that the inequality below is true, i tried some thing but got stuck, i tried to eliminate the absolute value $-1<\frac{x-y}{1-xy}<1$ and then solve for $x$ and $y$ with no luck...i do not want the answer to this problem but at least a method for solving this kind of exercises.
$x,y\in\Bbb R\ , |x|<1,|y|<1 \ \ \text{show that} \ \ \bigg|\frac{x-y}{1-xy}\bigg| < 1.$