Having trouble with this Limit problem below.?

Question

lim . . . .. . (x^2 - 9)/(x^3 - 27)
x=>3

Answer 1

That's suppose to give you 2/9.

Replace the 3 with the x variables and that's what you are going to get.

Answer 2

(x^2 - 9)/(x^3 - 27)=

=lim (x+3)*(x-3)/(x-3) (x^2 +3x + 9 )
x=>3
we cancel x-3 in numerator and denominator keeping in mind that x cannot be equal to 3.
thus we get

lim (x+3)/(x^2 + 3x +9 )
x=>3
we now put x=3 and get 6/27 which on simlification becomes
2/9 ..
thus ans is 2/9.