The right hand and left hand limit of the function $\left\{\begin{array}{l}\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, \mathrm{if} x\ne 0\\ 0 , \mathrm{if} x=0\end{array} \right.$ are respectively

Consider the following statements:
Statement $1:$$\underset{x\to 1}{\lim }\left[\frac{a{x}^2+bx+c}{c{x}^2+bx+a}\right]$ is $1$ (where $a+b+c\ne 0$)

Statement $2:$ $\underset{x\to -2}{\lim }\left[\frac{{\displaystyle \frac{1}{x}}+{\displaystyle \frac{1}{2}}}{x+2}\right]$ is $\frac{1}{4}$.