Example: What is the domain of the rational expression \[\dfrac{ x^2-x-6 }{ x^2+6x+8 }\]
Solution The denominator cannot equal zero, so let's solve \(x^2+6x+8=0\) and reject those values from the domain.
\[ \solve{ x^2+6x+8&=&0 \\(x+2)(x+4)&=&0 \\x=-2&\text{ or }&x=-4 } \] Thus, the domain (in interval notation) will be \((-\infty, -4)\cup(-4,-2)\cup(-2,\infty)\).