Consider the following limit $$\lim_{x\to 3}\frac{30 - 3 x - |x^2 - 10 x|}{|x^2- 100| - 91}$$ We can simplify this limit by rewriting it as an expression without absolute values as follows
$\lim_{x\to 3}$
We can then cancel off a common factor in the numerator and denominator, thus simplifying our limit to
$\lim_{x\to 3}$
We can then evaluate the limit directly and find that its value is