Bounds for $\frac{x-y}{x+y}$ How can I find upper and lower bounds for $\displaystyle\frac{x-y}{x+y}$? So I do see that
$$\frac{x-y}{x+y} = \frac{1}{x+y}\cdot(x-y) = \frac{x}{x+y} - \frac{y}{x+y} > \frac{1}{x+y} - \frac{1}{x+y} = \frac{0}{x+y} = 0$$
(is it correct?) but I don't get how to find the upper bound.

Look at pairs $(x,y)$ such that $x = 1-y$. For these pairs, $\frac{x-y}{x+y} = 1-2y$ and we have $\mbox{lim}_{y\rightarrow \pm\infty}(1-2y) = \mp \infty$.
