The function $g$ is defined by

where $b\in {\mathbb{R}}^{+}$ is a positive constant.

1. Show that

   $$g(x)=\frac{x-2b}{x+2b}$$

2. Prove $g$ is increasing for all values of $x$.

$x^2+bx-2b^2$ factorises

So does $x^2+4bx+4b^2$