## Calculus: Early Transcendentals 8th Edition

One example: $\frac{x^{2}+10}{x^{2}-4x+3}$
We will work out the denominator first. There must be vertical asymptotes at x=1 and x=3, so we can create a factored polynomial for the denominator= $(x-1)(x-3)$. Because we can create a horizontal asymptote by dividing coefficients of polynomials of the same highest degree, anything that has a $1x^{2}$ will work for us. Let's use $x^{2}+10$ (we could also just use $x^2$).