Question

Simplify
(1/√2+√3)+(1/√3+√4)+(

1/√4+√5)

Answer 1

$(\frac{1}{\sqrt{2}}+\sqrt{3})+(\frac{1}{\sqrt{3}}+\sqrt{4})+(\frac{1}{\sqrt{4}}+\sqrt{5})$

$\frac{\sqrt{2}}{2}+\sqrt{3}+\frac{1}{\sqrt{3}}+\sqrt{4}+\frac{1}{\sqrt{4}}+\sqrt{5}$

$\frac{\sqrt{2}}{2}+\sqrt{3}+\frac{1}{\sqrt{3}}+2+\frac{1}{2}+\sqrt{5}$

$\frac{\sqrt{2}}{2}+\sqrt{3}+\frac{\sqrt{3}}{3}+2+\frac{1}{2}+\sqrt{5}$

$\frac{\sqrt{2}}{2}+(\sqrt{3}+\frac{\sqrt{3}}{3})+(2+\frac{1}{2})+\sqrt{5}$

$\frac{\sqrt{2}}{2}+\frac{4\sqrt{3}}{3}+\frac{5}{2}+\sqrt{5}$