College Algebra 7th Edition

$0+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{\sqrt{5}}=0+\frac{\sqrt{3}}{3}+\frac{\sqrt{2}}{2}+\frac{\sqrt{15}}{5}$
We expand the sum: $\sum_{j=1}^{4}\sqrt{\frac{j-1}{j+1}}=\sqrt{\frac{0}{2}}+\sqrt{\frac{1}{3}}+\sqrt{\frac{2}{4}}+\sqrt{\frac{3}{5}}=0+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{\sqrt{5}}=0+\frac{\sqrt{3}}{3}+\frac{\sqrt{2}}{2}+\frac{\sqrt{15}}{5}$