Solving $x-\sqrt{(x^2-36)} = {(x-6)^2\over 2x+12}$. I have problem with this equation:
$$x-\sqrt{(x^2-36)} = {(x-6)^2\over 2x+12}$$
Any ideas on beatiful solving?

Assume $x+6=a$ and $x-6=b$
So LHS= $(a+b)/2-\sqrt{ab}=1/2 * (\sqrt a-\sqrt b)^2$. 
RHS= $b^2/2a$.
Hence, $b/\sqrt a=\sqrt a- \sqrt b$
Hence $b=a-\sqrt{ab}$ 
Therefore $\sqrt {ab}=a-b=12.$ Now, put  $a=12+b$ and solve $b(12+b)=144$.
Hope this helps. Correct me if I'm wrong! 
