Question

What are the removable and non-removable discontinuities, if any, of `f(x)=(x+2)/(x^2-3x-10)`?

Answer 1

Removable discontinuity at `x=-2`.
Non-removable discontinuity at `x=5`.

Explanation:

After factorization,

`f(x)=frac{x+2}{x^2-3x-10}`

`=frac{x+2}{(x+2)(x-5)}`

`lim_{x->-2}f(x)=-1/7`

`lim_{x->5}f(x)` is undefined.