Answer
$7\sqrt{3}-7\sqrt{2}$
Work Step by Step
$\displaystyle \frac{2}{\sqrt{2}+\sqrt{3}}\color{red}{ \cdot\frac{ \sqrt{2}-\sqrt{3}}{\sqrt{2}-\sqrt{3}} }=\frac{2(\sqrt{2}-\sqrt{3})}{(\sqrt{2})^{2}-(\sqrt{3})^{2}}$
$=\displaystyle \frac{2(\sqrt{2}-\sqrt{3})}{2-3}=\frac{2(\sqrt{2}-\sqrt{3})}{-1}\\\\=-2(\sqrt{2}-\sqrt{3})\\\\=-2\sqrt{2}+2\sqrt{3}$
$\sqrt{75}=\sqrt{25\cdot 3}=\sqrt{25}\cdot\sqrt{3}=5\sqrt{3}$
$\sqrt{50}=\sqrt{25\cdot 2}=\sqrt{25}\cdot\sqrt{2}=5\sqrt{2}$
$problem=-2\sqrt{2}+2\sqrt{3}+5\sqrt{3}-5\sqrt{2}$
... add like terms
$=7\sqrt{3}-7\sqrt{2}$
