Rational Functions

Rational Fractions
This is any function that can be defined as a rational fraction, or an algebraic fraction, showing that the numerator and denominator are polynomials.

Polynomials - is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, multiplication and non-negative integer exponents of variables.

Example of Rational Functions:

 

The general form of a rational function is p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0

It is also where ${\displaystyle P\,}$ and ${\displaystyle Q\,}$ are polynomials in ${\displaystyle x\,}$ and ${\displaystyle Q\,}$ is not the zero polynomial. The domain of ${\displaystyle f\,}$ is the set of all points ${\displaystyle x\,}$ for which the denominator ${\displaystyle Q(x)\,}$ is not zero.  


Examples that might help you in understanding the topic better:

1.) Teddy takes 15 minutes and Jake takes 60 minutes for the newspaper distribution in Jack. How long would it take for both, working together, to distribute the newspaper in Jack? 

Solution:

 

Teddy and Jake together will distribute the newspaper in Jack in 12 minutes.

Example 2:

Martin can do a job in 4 days and her assistant, Andrew can do the same job in 16 days. How long will it take for Andrew and Martin to complete the job, if they work together?