Ta có :

a.  Rút gọn Q.

 $Q=\frac{a}{\sqrt{a^{2}-b^{2}}}-\left ( 1+\frac{a}{\sqrt{a^{2}-b^{2}}} \right ):\frac{b}{a-\sqrt{a^{2}-b^{2}}}$ 

$Q=\frac{a}{\sqrt{a^{2}-b^{2}}}-\frac{a^{2}-(a^{2}-b^{2})}{b\sqrt{a^{2}-b^{2}}}$

$Q=\frac{a}{\sqrt{a^{2}-b^{2}}}-\frac{a^{2}-a^{2}+b^{2}}{b\sqrt{a^{2}-b^{2}}}$

$Q=\frac{a-b}{\sqrt{a^{2}-b^{2}}}$

$Q=\frac{(\sqrt{a-b})(\sqrt{a-b})}{(\sqrt{a-b})(\sqrt{a+b})}$

$Q=\frac{\sqrt{a-b}}{\sqrt{a+b}}$

Vậy  $Q=\frac{\sqrt{a-b}}{\sqrt{a+b}}$ .

b.  Khi a = 3b  , thay vào Q ta được :

$Q=\frac{\sqrt{3b-b}}{\sqrt{3b+b}}=\frac{\sqrt{2b}}{\sqrt{4b}}=\frac{1}{\sqrt{2}}$

Vậy khi a = 3b thì $Q=\frac{1}{\sqrt{2}}$ .