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Last updated at March 12, 2021 by Teachoo

Example 16 Prove that every rational function is continuous.Every Rational function π(π₯) is of the form π(π)= π(π)/π(π) where π(π₯) β 0 & π, π are polynomial functions Since π(π₯) & π(π₯) are polynomials, and we know that every polynomial function is continuous. Therefore, π(π) & π(π) both continuous By Algebra of continuous function If π, π are continuous , then π/π is continuous. Thus, Rational Function π(π₯)= π(π₯)/π(π₯) is continuous for all real numbers except at points where π(π) = 0