[latex] \lim_{x \to \ 5} \frac{2x^2 -11x +5 } {3x^2 - 14x - 5} [/latex] Найти пределы

[latex] \lim_{x \to 5} \frac{2x^2-11x+5}{3x^2-14x-5}=?\\\\2x^2-11x+5=2(x-5)(x-1/2)\\D=(-11)^2-4*2*5=121-40=81=9^2\\x_1= \frac{11+9}{2*2}= \frac{20}{4}=5\\x_2= \frac{11-9}{2*2}= \frac{2}{4}= \frac{1}{2}\\\\3x^2-14x-5=3(x-5)(x+1/3)\\D=(-14)^2-4*3(-5)=196+60=256=16^2\\x_1= \frac{14+16}{2*3}= \frac{30}{6}=5\\x_2= \frac{14-16}{2*3}= \frac{-2}{6}=- \frac{1}{3} \\\\ \lim_{x \to 5} \frac{2x^2-11x+5}{3x^2-14x-5}= \lim_{x\to 5} \frac{2(x-5)(x-1/2)}{3(x-5)(x-1/3)}= \lim_{x \to 5} \frac{2x-1}{3x-1}= [/latex] [latex]= \frac{2*5-1}{3*5-1}= \frac{10-1}{15-1}= \frac{9}{14} [/latex]