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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