Evaluate
\sqrt{5}-\sqrt{3}\approx 0.50401717
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\frac{2\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}
Rationalize the denominator of \frac{2}{\sqrt{5}+\sqrt{3}} by multiplying numerator and denominator by \sqrt{5}-\sqrt{3}.
\frac{2\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{2\left(\sqrt{5}-\sqrt{3}\right)}{5-3}
Square \sqrt{5}. Square \sqrt{3}.
\frac{2\left(\sqrt{5}-\sqrt{3}\right)}{2}
Subtract 3 from 5 to get 2.
\sqrt{5}-\sqrt{3}
Cancel out 2 and 2.
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