How Do You Divide Two Rational Expressions?

Note:

Dividing two rational expressions? Turn it into a multiplication problem by multiplying by the reciprocal of the second rational expression (the divisor)! This tutorial shows you how to do just that! Then, you'll see how to perform the multiplication and simplify to get you answer!

Keywords:

problem
rational expression
fraction
algebraic fraction
polynomial
divide
simplify
reciprocal
reciprocal rule of division
divisor
like terms
cancel
cancel out
multiply
numerator
denominator

Background Tutorials

Fraction Basics
- What's a Numerator and What's A Denominator?
  
  Numerators and denominators are the key ingredients that make fractions, so if you want to work with fractions, you have to know what numerators and denominators are. Lucky for you, this tutorial will teach you some great tricks for remembering what numerators and denominators are all about.
Dividing Real Numbers
- What's the Reciprocal Rule of Division?
  
  When you divide fractions, the trick is to rewrite division as a multiplication. But the truth is that you can always rewrite division as a multiplication, and in this tutorial you'll see the rule that makes that possible!
Horizontal and Vertical Lines
- How Do You Graph a Horizontal Line?
  
  To graph a horizontal line that goes through a given point, first plot that point. Then draw a straight line left and right that goes through the point, and you're done! To see this process in action, watch this tutorial!
Factors
- What's a Factor?
  
  Factors are a fundamental part of algebra, so it would be a great idea to know all about them. This tutorial can help! Take a look!
Factoring ax^2+bx+c
- How Do You Factor a Polynomial by Guessing and Checking?
  
  Factoring trinomials can by tricky, but this tutorial can help! Follow along as a trinomial is factored using the guess and check method. What, no possibilities work? The trinomial must be prime! Watch this tutorial and see what happens!
Difference of Squares and Cubes
- How Do You Factor a Polynomial Using Difference of Squares?
  
  Trying to factor a binomial with perfect square factors that are being subtracted? You have a difference of squares problem! Learn how to factor a binomial like this one by watching this tutorial.
Solving Quadratics by Factoring
- How Do You Solve a Quadratic Equation by Factoring?
  
  One of the many ways you can solve a quadratic equation is by factoring it. In this tutorial, you'll see how to factor a quadratic equation using the guess and check method of factoring. Then, use the zero product property to find the solution!
Simplifying Rational Expressions
- How Do You Simplify a Polynomial Over a Polynomial Using Opposite Binomial Factors?
  
  Simplifying a rational expression? You could factor the numerator and denominator and then cancel like factors. Learn what to do in this tutorial!
- What's a Rational Expression?
  
  Got a fraction with a polynomial in the numerator and denominator? You have a rational expression! Learn about rational expressions in this tutorial.
Excluded Values
- How Do You Find Excluded Values?
  
  Excluded values are values that will make the denominator of a fraction equal to 0. You can't divide by 0, so it's very important to find these excluded values when you're solving a rational expression. Follow along with this tutorial and learn how to find these excluded values!
- What's an Excluded Value?
  
  Excluded values are simply that: values that are excluded, or left out. These are values that will make the denominator of a rational expression equal to 0. Remember, you're not allowed to divide by 0, so these values are important to identify and exclude while solving. This tutorial shows you all about excluded values!