Find lim x->-3+ x-3/x^2 -9 =?

Question

Im still kind of confused please help

Answer 1

Do not forget parentheses, they are required in this instance.
lim x->-3+ (x-3)/(x^2 -9)

Note that the denominator can be factorized to (x+3)(x-3), and that the numerator can be "cancelled" with one of the factors (since x is never equal to +3).

Lim (x-3)/(x^2 -9)
x->-3+
=Lim (x-3)/((x+3)(x-3))
x->-3+
=Lim 1/(x+3)
x->-3+
=+∞
since x approches -3 from the right, where 1/(x+3) will remain positive as x->-3+.
Approaching from the left will make 1/(x+3) negative as x->-3-, hence lim=-∞.