Category Archives: MATH 111

Rational Expressions and Equations

What is a Rational Expression?

A rational number is a number that can be written as a quotient of integers. In other words, it’s any number that can create a nice and neat fraction. A rational expression is also a quotient, it’s just made up of polynomials. A rational expression can be written in the form P/Q. For example:

Evaluating Rational Expressions

Rational expressions have different numerical values depending on what values replace the variables. For example:

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Factoring Polynomials

Finding the Greatest Common Factor (GCF)

Finding the greatest common factor simply involves finding the largest number or term which will fit evenly into each number or term in a list. The way I like to go about this is by breaking each number or term into its smallest parts. Break each number down until you are multiplying together only prime numbers. All the numbers that they have in common should then be multiplied back up to create the GCF.

This is what it would look like in a list of numbers:

And this is what it would look like in a list of terms: