What is a rational equation?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
An equation that has a variable in the denominator, or more simply put, it’s an equation with fractions.
And solving equations with rational expressions can be using two different methods.
Method 1:
Simplify both sides of the equation by creating common denominators and then using Cross Multiplication to solve for the unknown variable.
I find that this method takes longer and can be somewhat tedious, so I prefer another method…
Method 2:
Multiply both sides of the equation by the least common denominator, and then solve for the unknown variable.
Why is this method easier?
Because we eliminate all the fractions right away!
Instantly we go from an equation that has fractions to one that doesn’t!
Brilliant!
Example of How to Solve Rational Equations
Moreover, you will find that the ability to eliminate fractions from an equation is a skill that will be incredibly important in future topics such as Systems of Equations and Partial Fractions.
So we take advantage of the fact that there is an equation, meaning whatever we do on one side we must do on the other, and multiply by the least common denominator (LCD) as Purple Math nicely states.
Together we will learn how to solve rational equations step by step; employing all of our skills and knowledge of polynomials and factoring to accomplish our goal.
Solving Equations (How-To) – Video
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