How to rationalize the denominator with x

Fractional terms: explanation, rules, etc.

Here you can learn what fraction terms are and how to calculate with them. Let's look at this:

  • A Explanation what fraction terms are and what rules apply.
  • Examples for expanding, shortening and calculating with fraction terms.
  • Tasks / exercises so that you can practice this yourself.
  • A Video to fraction terms.
  • A Question and answer area to this area.

Tip: You should already have a basic understanding of fractions. If you can't do this yet, please see the Fractional Calculation article.

Explanation: Fractional terms and rules

First of all, let's clarify what a fraction term actually is.


A fraction term is understood to be a fraction of numerator and denominator in which at least one variable (unknown) occurs in the denominator.

Some examples of fraction terms:

Fractional terms definition set:

Perhaps one or the other still remembers that one cannot divide by zero? Of course, this also applies to breaks. For this reason, it must be ensured that the denominator of a fraction does not become zero. The numbers which cannot be used are entered in the definition set.

Example definition set:

The definition set for the following fraction term is to be determined.


We take the denominator and set this to zero. With this we can calculate the number for x, which we are not allowed to use. We write this number in the definition set.


Fractional terms add, subtract, multiply and divide

In this section we look at examples of basic arithmetic operations using fraction terms.

Example 2: Fractional terms addition and expansion

Let's start by adding fractions. The simplest case of adding fraction terms is that the denominator is the same for all fractions. In this case you simply take over the denominator in the result and simply add the numerators with 4 + 6 = 10. Note: The definition set would be 0 here, because x = 0 must not be.

It gets a little more difficult when the denominators are different. In this case we are looking for a common denominator. To do this, we multiply the two output denominators by x2 Y = x2 y. The first fraction had x in the denominator2. Therefore we only expand with y. The second fraction only had y in the denominator, so we add x to the numerator2. Note: Both x and y cannot become zero.

Example 3: Fractional term subtraction and expansion

In this example, fractional terms are to be subtracted. We divided the front 3x by xy and then minus 1. The 1 in the back is nothing more than a fraction 1: 1. To find the main denominator, we multiply 1 xy and get xy as the new denominator. We still have to adjust the fractions (hence the red boxes).

We don't have to expand on the first fraction, because the denominator has not changed. With the second fraction, xy goes into the numerator. That is also logical, the xy: xy = 1. Now we can subtract the fraction: the denominator remains the same and the numerators are subtracted. If you like, you can now exclude x and shorten this out.

Note: x and y must not become zero either.

Example 4: multiplying fractional terms

Next we multiply a fraction term. It's very simple: the numerator is multiplied by the numerator and the denominator is multiplied by the denominator. Then we can shorten it with 2. Otherwise y and and u must not become zero.

Example 5: Dividing fractions

Let's see how to divide fractions. This is done by multiplying by the reciprocal. The numerator and denominator of the second fraction are swapped. Then we multiply the tenor by the numerator and we multiply the denominator by the denominator. Since the numerator and denominator are the same, it can be reduced to 1.

Dividing by zero is not permitted here either.

Exercises / Exercises Fractional Terms


Video fraction terms

Explanation and examples

We'll look at how to deal with fraction terms in the next video, under the heading Fractional Equations. Let's look at this:

  • An explanation of what fractions are.
  • Explanations of the definition set.
  • Example 1 is pre-calculated.
  • Example 2 is precalculated ..

Next video »

Questions with answers about fraction terms

In this section we look at typical questions with answers about fraction terms.

Q: What are the rules for fractional terms?

A: You should follow these rules for fractional terms.

  • First determines which numbers may not be used (definition set).
  • When adding fraction terms, a common denominator must be found and the fractions expanded accordingly. Then the denominator is retained and the numerators are added. Also add more under fractions.
  • When subtracting fraction terms, a common denominator must be found and the fractions expanded accordingly. Then the denominator is retained and the numerators are subtracted. Subtract more under fractions as well.
  • When multiplying fraction terms, numerator times numerator and denominator times denominator are calculated. You can learn the basics under multiplying fractions.
  • When dividing fraction terms, the reciprocal value is formed from the second fraction and then numerator times numerator and denominator times denominator are calculated. You can learn the basics under dividing fractions.

Q: What other topics should I check out?

A: Take a look at these topics: