You had \documentclas
(a final "s" was missing) and this will cause an error. Also, you had a4papter
and it should be a4paper
(this will only cause a warning, but it is still an incorrection and should be taken care of).
\documentclass[a4paper, 12pt]{article}
\usepackage{amsmath}
\begin{document}
find \(\lim_{x \to 3^+}\frac{2x}{x-3} \) and \( \lim_{x\to 3^-}\frac{2x}{x-3} \)
find
\[
\lim_{x \to 3^+}\frac{2x}{x-3} \text{ and } \lim_{x\to 3^-}\frac{2x}{x-3}
\]
\end{document}

Notice also that you have \lim
to appropriately typeset limits (correct font and spacing) and that you need \frac
to typeset fractions. In my example I also show both the in-line and the displayed forms of your expression.
As long as you are in a math expression, you don't have to close math mode and reopen it, so you can simply say
\( \lim_{x \to 3^+}\frac{2x}{x-3} \)
instead of
\( \lim_{x \to 3^+} \)\( \frac{2x}{x-3} \)
documentclass
anda4paper
.\documentclass
, and also\lim
and\frac
, i.e., with backslashes.