Solve Rational Equations

Depending on the type of problem, you can solve rational equations using one of two methods. It is important that you know both of them:

First, if the equation is set up as a proportion then you can cross multiply - this is the easier method. Otherwise, if there are multiple terms then you will need to multiply through by the LCD.

Tip: before trying to solve equations, make sure you know how to simplify rational equestions first.

Quick links:

Cross multiply
LCD method


Cross Multiply - When there is One Term on Each Side

Remember, you can only cross multiply when there is one term on each side. Otherwise, you need to use the LCD method.

Take a look at an example of cross multiplying:

Cross Multiply the Rational Equation

Many students find this process to be rather easy because they've done a process like this before. But be careful, don't try to cross multiply with every problem!

This process can only be used when there is one term on each side. It will basically look like "fraction" = "fraction."


If your equation does not fit that pattern, then you must...

Multiply LCD - Multiple Terms on One (or Both) Side(s)

Multiply by LCD to Solve Rational Equation  

We realize the LCD method might seem a little trickier than cross multiplying, but as we know, we can only use cross multiplication in special cases. Also, the algebra for the second problem was more complex If you had a hard time following the last couple steps, take a look at how to solve quadratic equations. In this example we used factoring.

You may also want to look at our page on simplifying rational expressions. There is a very common mistake that many students make, and you want to make sure to avoid it!

Excellent job solving rational equations. For other similar lessons, return to the Free Algebra Help page.

You may also want to visit the GradeA homepage for more free math help topics.




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