Evaluate
\sqrt{2}-\sqrt{5}\approx -0.821854415
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\frac{-3\left(\sqrt{2}-\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{2}-\sqrt{5}\right)}
Rationalize the denominator of \frac{-3}{\sqrt{2}+\sqrt{5}} by multiplying numerator and denominator by \sqrt{2}-\sqrt{5}.
\frac{-3\left(\sqrt{2}-\sqrt{5}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{5}\right)^{2}}
Consider \left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{2}-\sqrt{5}\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{2}-\sqrt{5}\right)}{2-5}
Square \sqrt{2}. Square \sqrt{5}.
\frac{-3\left(\sqrt{2}-\sqrt{5}\right)}{-3}
Subtract 5 from 2 to get -3.
\sqrt{2}-\sqrt{5}
Cancel out -3 and -3.
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