Evaluate
\sqrt{2}+\sqrt{5}\approx 3.65028154
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\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}
Rationalize the denominator of \frac{3}{\sqrt{5}-\sqrt{2}} by multiplying numerator and denominator by \sqrt{5}+\sqrt{2}.
\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{2}\right)^{2}}
Consider \left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\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{3\left(\sqrt{5}+\sqrt{2}\right)}{5-2}
Square \sqrt{5}. Square \sqrt{2}.
\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{3}
Subtract 2 from 5 to get 3.
\sqrt{5}+\sqrt{2}
Cancel out 3 and 3.
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