Limits of Rational Functions - Expii

Rational functions, like (x^2-4)/(x-2), are continuous on their domain, so the substitution rule applies when evaluating limits of rational functions within their domains. However, outside of the domain (at singularities), limits take more work and may require algebraic manipulation (especially factoring and "canceling" common factors in the numerator and denominator). For instance, (x^2-4)/(x-2) = x+2 for all x≠2, so its limit at x-2 is 4 by the substitution rule for polynomials.