Jambmaths question:
Rationalize $\frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}$
Option A:
$-5-2\sqrt{6}$
Option B:
$-5+3\sqrt{2}$
Option C:
$5-2\sqrt{3}$
Option D:
$5+2\sqrt{6}$
Jamb Maths Solution:
$\begin{align} & \frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}=\frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}\times \frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}+\sqrt{3}} \\ & \frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}=\frac{2+3+2\sqrt{6}}{2-3}=\frac{5+2\sqrt{6}}{-1} \\ & \frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}=-5-2\sqrt{6} \\\end{align}$
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