Question #0fc08

1 Answer
Cesareo R.
Sep 16, 2016

-1/18

Explanation:

(sqrt(2x+3)-sqrt(3x))/(x^2-3x)=(2x+3-3x)/((x^2-3x) (sqrt(2x+3)+sqrt(3x)))=
=(3-x)/(x(x-3)(sqrt(2x+3)+sqrt(3x)))=
-1/(x(sqrt(2x+3)+sqrt(3x))

so

lim_ (x->3) (sqrt(2x+3)-sqrt(3x))/(x^2-3x)=-1/(3 xx 2 xx 3)=-1/18

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