$\frac{x\sqrt[]{y}+y\sqrt[]{x}}{x-y}$$+\frac{x\sqrt[]{y}-y\sqrt[]{x}}{x+y}=$$\frac{(x\sqrt[]{y}+y\sqrt[]{x})(x+y)+(x\sqrt[]{y}-y\sqrt[]{x})(x-y)}{(x-y)(x+y)}=$$\frac{2x^2\sqrt[]{y}+2y^2\sqrt[]{x}}{(x-y)(x+y)}=$$\frac{2\sqrt[]{xy}(x\sqrt[]{x}+y\sqrt[]{y})}{(x-y)(x+y)}$