A rational function is the ratio of two polynomial functions.

A rational function can be simplified by factoring the polynomial functions and canceling the common factors
between numerator and denominator.

Domain of a rational function

For any value/values of x for which the denominator is zero, that value of x cannot be included in the domain of f(x)
because when p(x)=0,

Example

Simplify the function to lowest form and find its domain and range.

Answer

The first step to simplify the function is to factor the polynomials in the numerator and denominator.

The numerator can be factored as (x+2)(x+1)

The denominator will be zero when x=-1. Hence the domain of this function can be any real number except -1.
Mathematically it is written as R-{-1} where R is the set of all real numbers.

The range will be the set of all real numbers.

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