Question

Which of the following fractions is equal to $\frac{1}{\sqrt{3}-\sqrt{5}}$?

• A. $\frac{-(\sqrt{3}+\sqrt{5})}{4}$
• B. $\frac{-(\sqrt{3}+\sqrt{5})}{2}$
• C. $\frac{-(\sqrt{3}-\sqrt{5})}{2}$
• D. $\frac{(\sqrt{3}+\sqrt{5})}{4}$

Answer 1

The correct option is B

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

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