SolutionThe general rule for factoring rational expressions is to *factor everything* then we can cancel the multiplication we find with the division that makes up the rational expression. \[\dfrac{ x^2+x-12 }{ x^2-16 }=\dfrac{ (x+4)(x-3) }{ (x+4)(x-4) }\]Note that we have *common factors* of \(x+4\) in the numerator and denominator, so these factors cancel out, leaving us with \[\dfrac{ x-3 }{ x-4 }\]There are no further identical factors, so no further simplification is possible.