**4.1 Introduction**: A rational function is a division of two polynomial functions. Or we can say that it is a polynomial divided by another polynomial.

In the case of one variable, x, a rational function is a function of the form

*f*(*x*) = P (*x*)/ Q(*x*)

Where **P** and, **Q** are polynomial functions in ** x** and

**Example**

*f*(* x*) = *x*2 + *x* – 20,

*x*2 – *x* -12

The polynomials in the numerator and the denominator of the above function would factor like this:

*f*(*x*) = (*x* + 5) (*x* – 4),

(*x- *4) (*x* + 3)

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