Question

Which of the following fractions is equal to $\frac{1}{\sqrt{5}-\sqrt{7}}$?

• A. $\frac{-(\sqrt{5}+\sqrt{7})}{4}$
• B. $\frac{-(\sqrt{5}+\sqrt{7})}{2}$
• C. $\frac{-(\sqrt{5}-\sqrt{7})}{2}$
• D. $\frac{-(\sqrt{5}+\sqrt{7})}{8}$

Answer 1

The correct option is B

$\frac{-(\sqrt{5}+\sqrt{7})}{2}$

Rationalizing the expression we get,
$\frac{1}{\sqrt{5}-\sqrt{7}}=\frac{\sqrt{5}+\sqrt{7}}{(\sqrt{5}-\sqrt{7})(\sqrt{5}+\sqrt{7)}}$

=$\frac{\sqrt{5}+\sqrt{7}}{(\sqrt{5}{)}^2-(\sqrt{7}{)}^2}$

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