Rationalize the denominator: \(\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}} \cdot \frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}-\sqrt{3}}=\frac{2-\sqrt{6}-\sqrt{6}+3}{{\sqrt{2}}^{2}-{\sqrt{3}}^{2}}\).
\[\frac{2-\sqrt{6}-\sqrt{6}+3}{{\sqrt{2}}^{2}-{\sqrt{3}}^{2}}\]
Collect like terms.
\[\frac{(2+3)+(-\sqrt{6}-\sqrt{6})}{{\sqrt{2}}^{2}-{\sqrt{3}}^{2}}\]
Simplify \((2+3)+(-\sqrt{6}-\sqrt{6})\) to \(5-2\sqrt{6}\).
\[\frac{5-2\sqrt{6}}{{\sqrt{2}}^{2}-{\sqrt{3}}^{2}}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\frac{5-2\sqrt{6}}{2-{\sqrt{3}}^{2}}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\frac{5-2\sqrt{6}}{2-3}\]
Simplify \(2-3\) to \(-1\).
\[\frac{5-2\sqrt{6}}{-1}\]
Move the negative sign to the left.
\[-(5-2\sqrt{6})\]
Remove parentheses.
\[-5+2\sqrt{6}\]
Decimal Form: -0.101021
-5+2*sqrt(6)
