limit (x²-4)/x²-5x+6 x⇒ 2

lim (x²-4)/(x²-5x+6)
x⇒2
lim (x-2)(x+2)/(x-2)(x-3)
x⇒2
lim (x+2)/(x-3)
x⇒2
     (2+2)/(2-3)= 4/(-1)=-4

[tex] \lim_{x \to 2} \frac{x^2-4}{x^2-5x+6} = \lim_{x \to 2} \frac{(x+2)(x-2)}{(x-3)(x-2)}= \lim_{x \to 2} \frac{(x+2)}{(x-3)}= \frac{2+2}{2-3}=\frac{4}{-1}=-4[/tex]