oblicz granice

[gufox]

\(\displaystyle{ \lim_{x \to 3} \frac{2 \sqrt{x+1} - \sqrt{x+13} }{x ^{2}-9 }}\)

[wb]

\(\displaystyle{ \lim_{x \to 3} \frac{2 \sqrt{x+1} - \sqrt{x+13} }{x ^{2}-9 }=\lim_{x \to 3} \frac{(2 \sqrt{x+1} - \sqrt{x+13})(2 \sqrt{x+1} + \sqrt{x+13}) }{(x ^{2}-9)(2 \sqrt{x+1} + \sqrt{x+13 })}= \\ = \lim_{x \to 3} \frac{4x+4-x-13}{(x-3)(x+3)(2 \sqrt{x+1} + \sqrt{x+13 })} =\lim_{x \to 3} \frac{3(x-3)}{(x-3)(x+3)(2 \sqrt{x+1} + \sqrt{x+13 })}= \\ =\lim_{x \to 3} \frac{3}{(x+3)(2 \sqrt{x+1} + \sqrt{x+13 })}= \frac{3}{6 (2 2+4)}=...}\)