I’m trying to use the $varepsilon$–$delta$ definition of a limit to prove that

$$

lim_{x to 1} frac{1}{x+2} = 1/3.

$$

But I’m getting stuck on finding the correct $delta$. Here is my try:

begin{align*}

lvert f(x) – L rvert < varepsilon \

lvert frac{1}{x+2} – frac{1}{3} rvert < varepsilon \

lvert frac{x -1}{2 – x} rvert < 3varepsilon.

end{align*}

And then I’m not really sure what to do. How do you proceed from here?