Simplifying the expression $(\sqrt{5}+\sqrt{7})/(\sqrt{10}+\sqrt{14}+\sqrt{15}+\sqrt{21})$

Question

Alrite guys, this question might sound stupid, but I can't find a way to simplify this complicated expression:

$$\frac{\sqrt{5}+\sqrt{7}}{\sqrt{10}+\sqrt{14}+\sqrt{15}+\sqrt{21}}$$

I can't take the conjugate, nor I can factor the bottom.

Any help or hints?

Answer 1

Hint:

$$\sqrt{10}+\sqrt{14}+\sqrt{15}+\sqrt{21}$$

$$=\sqrt{2}(\sqrt{5}+\sqrt{7})+\sqrt{3}(\sqrt{5}+\sqrt{7})$$

$$=(\sqrt{5}+\sqrt{7})(\sqrt{2}+\sqrt{3})$$

Can you take it from here?