You're looking for the points where the function is not defined. Since this function is the ratio between two polynomial, the function is not defined where the denominator equals zero.
In this case, the denominator is [tex](x-3)(x+1)[/tex], so the discontinuity points can be found by imposing
[tex](x-3)(x+1)=0 \iff x-3=0 \lor x+1=0 \iff x=3 \lor x=-1[/tex]
