6. Сократите дробь: 1) √a+7/a-49; 2) 33-√33/√33; 3) a-2√3a+3/a-3.

1) $$ \frac{\sqrt{a}+7}{a-49} = \frac{\sqrt{a}+7}{(\sqrt{a}-7)(\sqrt{a}+7)} = \frac{1}{\sqrt{a}-7} $$

2) $$ \frac{33-\sqrt{33}}{\sqrt{33}} = \frac{\sqrt{33}(\sqrt{33}-1)}{\sqrt{33}} = \sqrt{33}-1 $$

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

Ответ: 1) $$ \frac{1}{\sqrt{a}-7} $$; 2) $$ \sqrt{33}-1 $$; 3) $$ \frac{\sqrt{a}-\sqrt{3}}{\sqrt{a}+3} $$