`Q=\frac{x^2+y^2-2xy}{x^2+y^2+2xy}.\frac{x^2+3xy+2y^2}{x^2-3xy+2y^2}:\frac{x^2-y^2}{x^2-4y^2}`
`=\frac{(x-y)^2}{(x+y)^2}.\frac{x(x+y)+2y(x+y)}{x(x-y)-2y(x-y)}:\frac{(x-y)(x+y)}{(x-2y)(x+2y)}`
`=\frac{(x-y)^2}{(x+y)^2}.\frac{(x+y)(x+2y)}{(x-y)(x-2y)}.\frac{(x-2y)(x+2y)}{(x-y)(x+y)}`
`=\frac{(x+2y)^2}{(x+y)^2}`