A rational expression is undefined when its denominator equals 0. Thus, we must find a denominator which equals 0 if x=5 or x=-7. The simplest polynomial that gives 0 when x=5 is 5−x, because 5−5=0. By the same reasoning, we find 7+x, because the 7+(-7)=0. For the denominator to be undefined for both x=5 and x=-7, the entire denominator must equal 0 when substituting x for these values. This is satisfied by the product (5−x)(7+x). The numerator can be any polynomial, for example, choose the rational expression (5−x)(7+x)2x.