## Algebraic Fractions

**Summary**

Algebraic fractions involve polynomials, usually expressed in terms of a polynomialdivided by other polynomials in– they may need to be added, subtracted, multiplied or divided. The rules are the same as for ordinary fractions:

To add or subtract, we make a common denominator then subtract the numerators.

To multiply, we just “multiply across”, so that the end result is

To divide, turn the dividing, second fraction, upside down, and multiply.

**Adding Algebraic Fractions**

The new denominator is

In the diagram above the arrows indicate multiplication

To illustrate, I will expand the brackets in the numerator and add

The numeratorcan be factorised intoThere is a common factor in numerator and denominator which can be cancelled.

**Subtracting Algebraic Fractions**

The new denominator is

In the diagram above the arrows indicate multiplication

To illustrate, I will expand the brackets in the numerator and subtract

There is no common factor.

**Multiplying Algebraic Fractions**

Just multiply across

There are no common factors so we cannot cancel.

**Dividing Algebraic Fractions**

Turn the second, dividing fraction upside down and multiply as above: