$(\frac{1}{\sqrt{a}-3}+\frac{1}{\sqrt{a}+3}).(1-\frac{3}{\sqrt{a}})$
$=$ $(\frac{\sqrt{a}+3}{(\sqrt{a}-3).(\sqrt{a}+3)}+\frac{\sqrt{a}-3}{(\sqrt{a}-3).(\sqrt{a}+3)}). \frac{\sqrt{a}-3}{\sqrt{a}}$
$=$ $\frac{\sqrt{a}+3+\sqrt{a}-3}{(\sqrt{a}-3).(\sqrt{a}+3)}.\frac{\sqrt{a}-3}{\sqrt{a}}$
$=$ $\frac{2\sqrt{a}}{(\sqrt{a}+3).\sqrt{a}}$
$=$ $\frac{2}{\sqrt{a}+3}$