<s>[INST] How to solve a limit that can be factored but doesn't help? I saw examples that can be factored, eliminating the part that causes the indetermination, none of this type. The other option is by rationalize but dont know how to apply it here.
$$\lim_{x \to 4} \frac{2x^2+7x+5}{x^2-16}$$
I tried by factoring, doesn't help
$$\lim_{x \rightarrow 4} \frac{(2x+5)(x+1)}{(x-4)(x+4)} \\$$
UPDATE: I make a mistake, the numerator is ${2x^2+7x+5}$ not ${x^2+7x+5}$, really sorry.
 [/INST] HINT
Your limit is in the form
$$\lim_{x \rightarrow 4} \frac{2x^2+7x+5}{(x-4)(x+4)} = \lim_{x \rightarrow 4} \frac{(2x+5)(x+1)}{(x+4)}\cdot \lim_{x \rightarrow 4} \frac{1}{x-4}$$
with
$$\lim_{x \rightarrow 4} \frac{(2x+5)(x+1)}{(x+4)} =\frac{65}{8}$$
then all boils down in that one
$$\lim_{x \rightarrow 4} \frac{1}{x-4} $$
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