Question
Rationalize the denominator $\frac{1}{\sqrt{5}-\sqrt{3}}$.
✓
Answer
The conjugate pair of $\sqrt{5}-\sqrt{3}$ is $\sqrt{5}+\sqrt{3}$.
$
\frac{1}{\sqrt{5}-\sqrt{3}}=\frac{1}{\sqrt{5}-\sqrt{3}} \times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{\sqrt{5}+\sqrt{3}}{(\sqrt{5})^2-(\sqrt{3})^2}=\frac{\sqrt{5}+\sqrt{3}}{5-3}=\frac{\sqrt{5}+\sqrt{3}}{2}
$
$
\frac{1}{\sqrt{5}-\sqrt{3}}=\frac{1}{\sqrt{5}-\sqrt{3}} \times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{\sqrt{5}+\sqrt{3}}{(\sqrt{5})^2-(\sqrt{3})^2}=\frac{\sqrt{5}+\sqrt{3}}{5-3}=\frac{\sqrt{5}+\sqrt{3}}{2}
$
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