Answer
$4\sqrt 3-4\sqrt 2$
Work Step by Step
To rationalize the denominator, we multiply both the numerator and the denominator of the expression by $\sqrt 3-\sqrt 2$ and then simplify:
$\frac{4}{\sqrt 3+\sqrt 2}\times\frac{\sqrt 3-\sqrt 2}{\sqrt 3-\sqrt 2}$
=$\frac{4(\sqrt 3-\sqrt 2)}{(\sqrt 3+\sqrt 2)(\sqrt 3-\sqrt 2)}$
=$\frac{4\sqrt 3-4\sqrt 2}{(\sqrt 3)^{2}-(\sqrt 2)^{2}}$
=$\frac{4\sqrt 3-4\sqrt 2}{3-2}$
=$\frac{4\sqrt 3-4\sqrt 2}{1}$
=$4\sqrt 3-4\sqrt 2$
