x-gt-0-y-gt-0-prove-that-xy-x-y-lt-x-

Question Number 84532 by john santu last updated on 14/Mar/20

x > 0, y > 0 prove that

\frac{xy}{x + y} < x

Commented by mr W last updated on 14/Mar/20

\Rightarrow y < x + y

\Rightarrow \frac{y}{x + y} < 1

\Rightarrow \frac{x y}{x + y} < x

Answered by TANMAY PANACEA last updated on 14/Mar/20

\frac{x y}{x + y} - x

\frac{x y - x^{2} - x y}{x + y}

\frac{- x^{2}}{x + y} < 0 s o \frac{x y}{x + y} < x