# What is Clearing Denominators in Rational Equations?

Jan 27, 2015

I have created a video answer (with different examples) here: Clearing Fractions in Equations

Clearing denominators in rational equation is also known as clearing fraction in an equation. There are many times when a problem becomes easier to solve if you don’t have to worry about adding and subtracting fractions.

To clear the denominators you will need to multiply both sides of the equation by the smallest number both denominators divide evenly into.

Lets look at the problem:

$\frac{x}{2} + 5 = \frac{x}{3} + 8$

First we need to find the smallest number both 2 and 3 go into (or the LCD), which would be 6. Then we multiply both sides of the equation by that number.

$6 \left(\frac{x}{2} + 5\right) = 6 \left(\frac{x}{3} + 8\right)$

Using the distributive property, simplify the equation.

$\left(6 \cdot \frac{x}{2}\right) + \left(6 \cdot 30\right) = \left(6 \cdot \frac{x}{3}\right) + \left(6 \cdot 8\right)$

$3 x + 30 = 2 x + 48$

Now solving the equation as usual, we get

$x = 18$