To divide two rational functions, the operation is performed by dividing their defining rational expressions. Because rational functions are evaluated by their rational expressions, the division of the functions follows the identical procedure used for dividing rational expressions. The resulting quotient is found by rewriting the division as multiplication by the reciprocal of the second rational expression, and then applying the standard techniques for multiplying and simplifying rational expressions.

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A rational function is a mathematical function defined by a rational expression. It is typically written in the form $$R(x) = \frac{p(x)}{q(x)}$$, where both $$p(x)$$ and $$q(x)$$ are polynomial functions, and the denominator polynomial $$q(x)$$ is not equal to zero. Just as a rational expression is the ratio of two polynomials, a rational function assigns output values based on the ratio of two polynomial functions.

Rational Function

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