A cura di: Administrator

Limite in forma indeterminata $infty – infty$

$lim_{x rightarrow 3} (frac{5}{x^2-x-6}-frac{2}{x^2-4x+3}) =$$lim_{x rightarrow 3} [frac{5}{(x-3)(x+2)}-frac{2}{(x-3)(x-1)}] =$$lim_{x rightarrow 3} [frac{1}{x-3}cdot (frac{5}{x+2}-frac{2}{x-1})] =$$lim_{x rightarrow 3} [frac{1}{x-3}cdot frac{5x-5-2x-4}{(x+2)(x-1)}] =$$lim_{x rightarrow 3} frac{3x-9}{(x-3)(x+2)(x-1)} =$$lim_{x rightarrow 3} frac{3}{(x+2)(x-1)} = frac{3}{10}$