Question

How do you find the limit of `(x^2-9)/(x^2+2x-3)` as x approaches 3?

Answer 1

`=lim_(x->3) ((x + 3)(x - 3))/((x + 3)(x - 1)`

`=lim_(x->3) (x- 3)/(x - 1)`

`=( 3 - 3)/(3 - 1)`

`=0`

Note that you could have substituted in `x = 3` directly, but the above method is a good way of practicing when you will have problems that don't work that nicely.

Hopefully this helps!