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

$$\mathrm{x}>0,\mathrm{y}>0\mathrm{prove}\mathrm{that}$$ $$\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}<\mathrm{x}$$

Commented bymr W last updated on 14/Mar/20

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

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

$$\frac{xy}{x+y}-x$$ $$\frac{xy-x^2-xy}{x+y}$$ $$\frac{-x^2}{x+y}<0so\frac{xy}{x+y}<x$$

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