Question

$lim_{x to 2} ( frac{1}{x-2} - frac{12}{ x^{3}-8 } )$

Answer 1

$lim_{x to 2} ( frac{1}{x-2}- frac{12}{x^3-8} )= lim_{x to 2} (frac{1}{x-2} - frac{12}{(x-2)(x^2+2x+4)} )=\ \ \ = lim_{x to 2} frac{x^2+2x+4-12}{(x-2)(x^2+2x+4)} = lim_{x to 2} frac{x^2+2x-8}{(x-2)(x^2+2x+4)} = \ \ \ =lim_{x to 2} frac{(x+4)(x-2)}{(x-2)(x^2+2x+4)} = lim_{x to 2} frac{x+4}{x^2+2x+4} = frac{2+4}{2^2+2*2+4} = frac{1}{2}$

Answer 2

OK !