$\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{x}{x-9}=\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{x}{(\sqrt{x}-3)(\sqrt{x}+3)}=\frac{\sqrt{x}(\sqrt{x}+3)-x}{(\sqrt{x}-3)(\sqrt{x}+3)}=\frac{x+3\sqrt{x}-x}{x-9}=\frac{3\sqrt{x}}{x-9}$

$(\frac{\sqrt{b}}{\sqrt{b}-\sqrt{c}}+\frac{\sqrt{b}}{\sqrt{c}}):\frac{\sqrt{b}}{\sqrt{b}-\sqrt{c}}=\frac{\sqrt{b}\ast \sqrt{c}+\sqrt{b}(\sqrt{b}-\sqrt{c})}{\sqrt{c}(\sqrt{b}-\sqrt{c})}\ast \frac{\sqrt{b}-\sqrt{c}}{\sqrt{b}}=\frac{\sqrt{bc}+b-\sqrt{bc}}{\sqrt{c}}\ast \frac{1}{\sqrt{b}}=\frac{b}{\sqrt{bc}}=\frac{\sqrt{b}}{\sqrt{c}}=\sqrt{\frac{b}{c}}$