Cancelling denominators

So, we can do almost anything to an equation as long as we do it to both sides of the equation. If the equation contains fractional terms, the easiest way to solve the equation is to first get rid of these. That is, to first cancel the denominators.

Example 1

Solve the equation

a simple equation where we get rid of the denominator by multiplying it and by doing so, cancelling it.

There are now two fractional terms. Each has a denominator of 3. We can solve it in two ways:

Method A: Multiply the entire equation by 3, which eliminates all denominators.

Method B: Both terms are thirds, so we can first add the terms together.

Both ways are correct methods to solve the equation.

Now the terms have a different denominators. We can again solve this equation in two ways.

Method A: Expand the terms to the same denominator and then remove the denominator.

Method B: Note that the denominators of terms are factors of the number 6. Let's multiply the equation directly by 6.

The denominators of the terms are factors of the number 10. We can multiply the equation by 10

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