[latex] \lim_{n \to5} \frac{ x^{2} -11x+30}{ x^{2} -25} [/latex]

[latex] lim \ x-> 5 \ \ \ \frac{x^2-11x+30}{x^2-25}\\ lim \ x-> 5 \ \ \ \frac{x^2-11x+30}{x^2-25}\\ lim \ x-> 5 \ \ \ \frac{(x-6)(x-5)}{(x-5)(x+5)}\\ lim \ x-> 5 \ \ \ \frac{x-6}{x+5} = -\frac{1}{10}[/latex]

[latex]\lim\limits_{x\to5}\frac{x^2-11x+30}{x^2-25}=\frac00=\\= \lim\limits_{x\to5}\frac{x^2-5x-6x+30}{(x-5)\cdot(x+5)}=\\ =\lim\limits_{x\to5}\frac{x\cdot(x-5)-6\cdot(x-5)}{(x-5)\cdot(x+5)}=\\= \lim\limits_{x\to5}\frac{(x-5)\cdot(x-6)}{(x-5)\cdot(x+5)}=\\=\lim\limits_{x\to5}\frac{x-6}{x+5}=\frac{5-6}{5+6}=-\frac{1}{10}=\\ =-0,1.;\\ \lim\limits_{x\to5}\frac{x^2-11x+30}{x^2-25}=-\frac{1}{10}=-0,1 [/latex]