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MMO 214 Moscow MO 1952 |x| < 1, |y| < 1 => |(x - y/(1-xy)| <1

Source:

August 8, 2019
inequalitiesalgebraabsolute valueMoscow

Problem Statement

Prove that if ∣x∣<1|x| < 1 and ∣y∣<1|y| < 1, then ∣x−y1−xy∣<1\left|\frac{x - y}{1 -xy}\right|< 1.
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