\(a-\sqrt{ab}-6b=0\Rightarrow a-3\sqrt{ab}+2\sqrt{ab}-6b=0\)
=> \(\sqrt{a}.\left(\sqrt{a}-3\sqrt{b}\right)+2\sqrt{b}.\left(\sqrt{a}-3\sqrt{b}\right)=0\)
=> \(\left(\sqrt{a}+2\sqrt{b}\right).\left(\sqrt{a}-3\sqrt{b}\right)=0\)=> \(\sqrt{a}-3\sqrt{b}=0\) vì a; b > 0 nên \(\sqrt{a}+2\sqrt{b}>0\)
<=> \(\sqrt{a}=3\sqrt{b}\Rightarrow a=9b\)
Vậy \(P=\frac{9b+b}{9b+\sqrt{9b^2}+b}=\frac{10b}{13b}=\frac{10}{13}\)