# Algebraic fractions

**Algebraic fractions**

The rules which apply to the numerical fractions are the same at the algebraic fractions. The following are examples of algebraic fractions:

If the numerator and the denominator is multiplied or divided by the same number or term, the equivalent fraction is produced.

For example,

**Simplifying algebraic fractions**

Algebraic fractions are simplified in the same way as numerical fractions. As previously mentioned, this is carried out by dividing the numerator and the denominator using the same factors.

For example:

There maybe occasions where the numerator and denominator will need to be factorised because the algebraic fraction is simplified.

For example:

Another way of writing a fraction is as follows:

**Multiplying and dividing algebraic fractions**

The same rules used for numerical fractions are used to multiply and divide algebraic fractions.

Therefore:

and,

**Adding algebraic fractions**

Again, the same method for adding numerical fractions is used for algebraic fractions.

Therefore:

**Subtracting algebraic fractions**

Again, the same method for subtracting numerical fractions is used for algebraic fractions.

Therefore: