Proving equation is true Here is a question

Show that if $x&gt;0$,$y&gt;0$ than:


  $$\frac{1}{x}+\frac{1}{y}\geq\frac{4}{{x+y}}$$


How would you solve/start this?
$\frac{x}{y}+\frac{y}{x} \geq 2$
Hint One way is simply to show that $$\frac1x+\frac1y-\frac{4}{x+y}\ge 0.$$

Then the rest is just simple algebra.