Exercise
Simplify the expression:
\frac{\sqrt{3}-\sqrt{2}}{\sqrt{2}+\sqrt{3}}
Final Answer
Solution
Using Powers and Roots rules we get:
\frac{\sqrt{3}-\sqrt{2}}{\sqrt{2}+\sqrt{3}}=
=\frac{(\sqrt{3}-\sqrt{2})(\sqrt{2}-\sqrt{3})}{(\sqrt{2}+\sqrt{3})(\sqrt{2}-\sqrt{3})}=
=\frac{-{(\sqrt{2}-\sqrt{3})}^2}{2-3}=
={(\sqrt{2}-\sqrt{3})}^2=
=2-2\cdot\sqrt{2}\sqrt{3}+3=
=5-2\sqrt{6}