Question

Помогите решить
Lim x=3
(6/(x^2-9)-1/(x-3))

Answer 1

$lim_{x to 3} ( frac{6}{ x^{2} -9}- frac{1}{x-3} ) = frac{6}{ 3^{2}-9 } - frac{1}{3-3} = frac{6}{0} - frac{1}{0}$
$lim_{x to 3}( frac{6}{(x-3)*(x+3)}- frac{1 ^{(x+3} }{x-3} )= lim_{x to 3} frac{6-x-3}{(x-3)*(x+3)} =$
$= lim_{x to 3} frac{-x+3}{(x-3)*(x+3)} = lim_{x to 3} frac{-(x-3)}{(x-3)*(x+3)} = lim_{x to 3} frac{-1}{x+3} = frac{-1}{3+3} =$
$=- frac{1}{6}$