What is the simplest form of \( \frac{2 \sqrt{2}}{\sqrt{3}-\sqrt{2}} \) ?

To simplify \( \frac{2 \sqrt{2}}{\sqrt{3}-\sqrt{2}} \), we can rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator, \( \sqrt{3} + \sqrt{2} \): \[ \frac{2 \sqrt{2} (\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})} \] In the denominator, \( (\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) \) simplifies to \( 3 - 2 = 1 \). Thus, we have: \[ 2 \sqrt{2} (\sqrt{3} + \sqrt{2}) \] Now, distributing \( 2 \sqrt{2} \): \[ = 2 \sqrt{6} + 4 \] So the simplified form is: \[ \boxed{2\sqrt{6} + 4} \]