How Do You Divide Two Rational Expressions?

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

  • Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

      • What's the Reciprocal Rule of Division?What's the Reciprocal Rule of Division?

      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!

  • Interpret parts of an expression, such as terms, factors, and coefficients.

      • What's a Factor?What's a Factor?

      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!

  • Use the structure of an expression to identify ways to rewrite it.

  • Factor a quadratic expression to reveal the zeros of the function it defines.

      • How Do You Solve a Quadratic Equation by Factoring?How Do You Solve a Quadratic Equation 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!

      • How Do You Factor a Polynomial by Guessing and Checking?How Do You Factor a Polynomial by Guessing and Checking?

      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!

  • Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + (r(x)/b(x)), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

  • Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

      • What's a Rational Expression?What's a Rational Expression?

      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.

  • Graph linear and quadratic functions and show intercepts, maxima, and minima.

      • How Do You Graph a Horizontal Line?How Do You Graph a Horizontal Line?

      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!