lim x menuju 3 x^2-10x+21/x^2-9

Limit bentuk 0/0

lim(x-> 3)  (x² - 10x + 21) /(x² - 9)
lim (x->3)  (x -3)(x- 7) /(x - 3)(x+3)
lim (x->3)  (x-7)/(x+3)
x= 3 --> (3-7)/(3+3)= (-4)/(6)= -2/3

[tex]$\begin{align}\lim_{x\to3}\frac{x^2-10x+21}{x^2-9}&=\lim_{x\to3}\frac{(x-7)(x-3)}{(x+3)(x-3)}\\&=\lim_{x\to3}\frac{x-7}{x+3}\\&=\frac{3-7}{3+3}\\&=\frac{-4}{6}\\&=\boxed{-\frac23}\end[/tex]