\( \def\dfrac#1#2{\displaystyle\frac{#1}{#2}} \def\solve#1{\begin{array}{rcl}#1\end{array} } \)

Home / 06 Rational Functions / 01 Domain Of Rational Expressions

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 \((-\infty, -4)\cup(-4,-2)\cup(-2,\infty)\).