Answer
domain : $\{\ x \ |\ \ x\neq-4, \ x\neq 5 \ \}$
interval notation: $(-\infty,-4)\cup(-4,5)\cup(5,\infty)$
Work Step by Step
See example 1.
Division by 0 is undefined, so
f(x) will be defined for all real numbers except for
the number(s) x that yield zero in the denominator:
$(x-5)(x+4)=0$
$x=5\ $ or $x=-4\qquad $(zero product principle)
domain : $\{\ x \ |\ \ x\neq-4, \ x\neq 5 \ \}$
interval notation: $(-\infty,-4)\cup(-4,5)\cup(5,\infty)$
