(√7-√5)·(3√7+3√5)=(√7-√5)·3·(√7+√5)
=3(7-5)
=6
[tex] \frac{1}{2+\sqrt{3}+\sqrt{5}}=\frac{2-\sqrt{3}-\sqrt{5}}{(2-\sqrt{3}-\sqrt{5})(2+\sqrt{3}+\sqrt{5})} \\ \\
=\frac{2-\sqrt{3}-\sqrt{5}}{4+2\sqrt{3}+2\sqrt{5}-2\sqrt{3}-3-\sqrt{15}-2\sqrt{5}-\sqrt{15}-5} \\ \\
= \frac{2-\sqrt{3}-\sqrt{5}}{4-3-5-2 \sqrt{15}}=-\frac{2-\sqrt{3}-\sqrt{5}}{-4-2 \sqrt{15}} [/tex]