lower bound on $xy/(x+y)?$ I am looking forward to a lower bound on $x*y/(x+y),$ where both of $x\geq 1$ and $y\geq 1$ are real.
The upper bound on $x*y/(x+y)$ is obvious, for example $x$ or $y$. But a lower bound is not very obvious to me. I want a simple lower bound, which is not very complex.
Could anyone pass some wisdom to me? 
Thanks a lot in advance..

Flip it over. After some simplification, we get $\dfrac{1}{y}+\dfrac{1}{x}$. It is not hard to find an upper bound for this.
