$rac{x^2y+xy^2}{x^2y^2+x^2y^2} = rac{(x imes x imes y) + (x imes y imes y)}{(x imes x imes x imes y imes y) + (x imes x imes y imes y imes y)} = rac{xy(x+y)}{x^2y^2(x+y)} = rac{xy}{x^2y^2} = rac{xy}{x imes x imes y imes y} = rac{1}{xy}$