## Algebraic Fractions

Summary

Algebraic fractions involve polynomials, usually expressed in terms of a polynomial divided 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. 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 numerator can be factorised into There 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:  