Question

Помогите с решением предела

Answer 1

$\lim_{x \to 3} \bigg ( \dfrac{6}{x^2 - 9} - \dfrac{1}{x - 3} \bigg ) = \lim_{x \to 3} \bigg ( \dfrac{6}{(x - 3)(x + 3)} - \dfrac{1}{x - 3} \bigg) = \\ \\ \lim_{x \to 3} \dfrac{6 - x - 3 }{(x - 3)(x + 3)} = \lim_{x \to 3} \dfrac{-(x - 3)}{(x - 3)(x + 3)} = \\ \\ = \lim_{x \to 3} \dfrac{-1}{x + 3 } = -\dfrac{1}{3 + 3} = -\dfrac{1}{6}$

Answer 2

Lim[x->3](6/(x^2 - 9) - 1/(x-3)) = lim[x->3](6/(x^2 - 9) - (x+3)/(x^2 - 9)) = lim[x->3]((6 - x - 3)/(x^2 - 9)) = lim[x->3]((3 - x)/((x-3)*(x+3)))) = lim[x->3](-1/(x+3)) = -1/6

Ответ: -1/6