Answer
The slope of the curve at $x=0$ is $2$.
Work Step by Step
The slope $m$ of the tangent line of the curve $f(x)$ at $A(a,b)$ is also the slope of the curve at that point, which is calculated by $$m=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}$$
$$f(x)=\frac{x-1}{x+1}\hspace{1cm}x=0$$
To calculate the slope of the curve at $x=0$, we apply the above formula:
$$m=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}$$
Here $a=x=0$
$$m=\lim_{h\to0}\frac{f(h+0)-f(0)}{h}=\lim_{h\to0}\frac{f(h)-f(0)}{h}$$
$$m=\lim_{h\to0}\frac{\frac{h-1}{h+1}-\frac{0-1}{0+1}}{h}=\lim_{h\to0}\frac{\frac{h-1}{h+1}+1}{h}=\lim_{h\to0}\frac{\frac{h-1+h+1}{h+1}}{h}$$
$$m=\lim_{h\to0}\frac{2h}{h(h+1)}=\lim_{h\to0}\frac{2}{h+1}$$
$$m=\frac{2}{0+1}=2$$
