How do you find lim (x^2+4)/(x^2-4) as x->2?

The function has vertical asymptotes at x =-2 and x = +2. Informally, $x \to \infty$ as $x \to 2$.
Furthermore, as $x \to \pm \infty$, the function $\to$ 1, because the coefficients of the highest power of $x$ in the numerator polynomial is the same as that in the denominator polynomial.