Question

How do you evaluate the limit `(1/x^2-1/9)/(x-3)` as x approaches `3`?

Answer 1

`-2/27`

Explanation:

`(1/x^2-1/9)/(x-3) = -(x^2-9)/(9 x^2(x-3)) =-((x+3)(x-3))/(9x^2(x-3)) =-(x+3)/(9x^2)`

so

`lim_(x->3)(1/x^2-1/9)/(x-3) = lim_(x->3)-(x+3)/(9x^2)=-2/27`