Question

25 баллов. Сократите дроби

Answer 1

$1)\frac{\sqrt{3}-3 }{3\sqrt{2}-\sqrt{6}}=\frac{\sqrt{3}-(\sqrt{3})^{2}}{(\sqrt{3})^{2}*\sqrt{2}-\sqrt{3}*\sqrt{2}} =\frac{\sqrt{3}(1-\sqrt{3})}{\sqrt{3}*\sqrt{2}(\sqrt{3} -1)}=\boxed{-\frac{1}{\sqrt{2}}}$

$2)\frac{9a-b^{2} }{9a-6b\sqrt{a}+b^{2}}=\frac{(3\sqrt{a})^{2}-b^{2}}{(3\sqrt{a})^{2}-2*3\sqrt{a}*b+b^{2}}=\frac{(3\sqrt{a}-b)(3\sqrt{a}+b)}{(3\sqrt{a}-b)^{2}}=\boxed{\frac{3\sqrt{a}+b }{3\sqrt{a}-b}}$