Find all the vertical and horizontal asymptotes for (x^2+4x+3)/(x^2-1)

All I can figure out is that if the degree of the denominator is bigger than the numerator, then y=0. But I don't know if that's right! Please help. Thank you!

vertical at +-1 (see denominator)

Horizotal: divide the numerator by the largest power of x in the denominator, one gets 1+4/x+3/x^2
so as x gets very large +, horizonal tends to 1.
and as x gets very large -, horizonal goes to 1.