Limit of a function with powers

Question

I don't think a similar question has been asked yet, but I've been stumped by the following problem and was hoping maybe someone could spare a few moments to help me out.

$\lim_{x\to\:3}\left(\frac{5x^2-8x-13}{x^2-5}\right)ln\left(\frac{4x+2}{4x+5}\right)$

I can't use l'hopital to solve this problem and even online limit calculators can't seem to handle this one quite well. I am very grateful for your help!

Best Regards

Dave

Answer 1

Hint 1: Sums, products, quotients and compositions of continuous functions are continuous functions.

Hint 2: Given a function $h:X\subset\Bbb{R}\to\Bbb{R}$ such that $h$ is continuous at $p\in X'$, we have that $$\lim_{x\to p} h(x) = h(p)$$ What it means? It means that, if $h$ is continuous in $p$ and we want to calculate this limit, then we just have to calculate $h(p)$.

Answer 2

I don't see any problem with this limit, the point is defined for the function.