\(\quad\displaystyle\lim_{x\to4}\frac{\sqrt{x^2+9}-5}{\sqrt{3x-3}-3}\\ =\displaystyle\lim_{x\to4}\frac{(\sqrt{x^2+9}-5)(\sqrt{3x-3}+3)(\sqrt{x^2+9}+5)} {(\sqrt{3x-3}-3)(\sqrt{3x-3}+3)(\sqrt{x^2+9}+5)}\\ =\displaystyle\lim_{x\to4}\frac{(x^2+9-25)(\sqrt{3x-3}+3)}{(3x-3-9)(\sqrt{x^2+9}+5)}\\ =\displaystyle\lim_{x\to4}\frac{(x^2-16)(\sqrt{3x-3}+3)}{(3x-12)(\sqrt{x^2+9}+5)}\\ =\displaystyle\lim_{x\to4}\frac{(x-4)(x+4)(\sqrt{3x-3}+3)}{3(x-4)(\sqrt{x^2+9}+5)}\\ =\displaystyle\lim_{x\to4}\frac{(x+4)(\sqrt{3x-3}+3)}{3(\sqrt{x^2+9}+5)}\\ =\large\frac{8.6}{3.10}=\frac{16}{10}=1,6\qquad\qquad\qquad\qquad\tiny gricha - 18.10.24 \)