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a fraction can only be undefined if the denominator equals zero. the value and sign of the numerator does not matter at all.  first of all, remember that zero itself is neither positive nor negative, so neither p nor q nor s could equal zero by itself. the sum [positive] + [positive] can never be zero, but the sum [positive] + [negative] could be zero: (q + s) and (p + s) could be zero, so fractions (a) and (b) could be undefined. the differences [positive] – [negative] or [negative] – [positive] can never be zero, but [positive] – [positive] could be zero: (p – q) could be zero, which means fraction (e) could be undefined. fractions (a), (b), and (e) are the only ones that could be undefined.