Complex sentence: The sum, product, or quotient (excepting division by the zero polynomial) of two rational functions is itself a rational function: however, the process of reduction to standard form may inadvertently result in the removal of such discontinuities unless care is taken.
Split into simpler sentences: The sum, product, or quotient (excepting division by the zero polynomial) of two rational functions is itself a rational function. However, the process of reduction to standard form may inadvertently result in the removal of such singularities unless care is taken.