Lim x2-2x-3/x2-9
X->3

[tex]\displaystyle \lim_{x\rightarrow 3} \frac{x^2-2x-3}{x^2-9}= \lim_{x\rightarrow 3} \frac{x^2-2x-3}{(x-3)(x+3)}=\lim_{x\rightarrow 3} \frac{(x-3)(x+1)}{(x-3)(x+3)}=\\\\=\lim_{x\rightarrow 3} \frac{x+1}{x+3}= \frac{4}{6} = \frac{2}{3} [/tex]