The value of $$\frac{x}{x-y}+\frac{y}{x+y}+\frac{2xy}{y^{2}-x^{2}}$$​ is

Correct option is B

Given:
​$$\frac{x}{x-y}+\frac{y}{x+y}+\frac{2xy}{y^{2}-x^{2}}\\ \ \\y^{2}-x^{2} = (y-x)(y+x) = -(x-y)(x+y)\\ \ \\\frac{2xy}{y^{2}-x^{2}} = -\frac{2xy}{(x-y)(x+y)}\\ \ \\\frac{x(x+y) + y(x-y) - 2xy}{(x-y)(x+y)}\\ \ \\x(x+y) = x^{2}+xy,\quad y(x-y)=xy-y^{2}\\ \ \\x^{2}+xy+xy-y^{2}-2xy = x^{2}-y^{2}\\ \ \\\frac{x^{2}-y^{2}}{(x-y)(x+y)} = \frac{x^{2}-y^{2}}{x^{2}-y^{2}} = 1\\ \ \\{1}$$ 

Altetnate solution: