Answer:
Step-by-step explanation:
[tex]\frac{\sqrt{x-y}}{\sqrt{x+y}-\sqrt{x-y}}-\frac{\sqrt{x-y}}{\sqrt{x+y}+\sqrt{x-y}}\\\\=\frac{\sqrt{x-y}*(\sqrt{x+y}+\sqrt{x-y})-(\sqrt{x-y})*(\sqrt{x+y}-\sqrt{x-y})}{(\sqrt{x+y}-\sqrt{x-y})*(\sqrt{x+y}+\sqrt{x-y})}\\\\=\frac{\sqrt{x-y}*(\sqrt{x+y}+\sqrt{x-y}-\sqrt{x+y}+\sqrt{x-y})}{(\sqrt{x+y})^2-(\sqrt{x-y)^{2}}}\\\\=\frac{\sqrt{x-y}*2\sqrt{x-y}}{x+y-x+y}\\\\=2*\frac{x-y}{2y}=\frac{x-y}{y}\\\\(\frac{\sqrt{x-y}}{\sqrt{x+y}-\sqrt{x-y}}-\frac{\sqrt{x-y}}{\sqrt{x+y}+\sqrt{x-y}})*y=\frac{x-y}{y}*y\\\\=x-y[/tex]
