Welcome to this deck on algebraic fractions. An algebraic fraction is simply a fraction that contains algebraic expressions in its numerator, its denominator, or both. They might look complicated, but they follow all the same rules as the numerical fractions you're already familiar with. In this deck, we'll cover how to simplify, multiply, divide, add, and subtract them, as well as how to solve equations that involve them.

Let's start with simplifying. The key to simplifying any fraction, whether it's numerical or algebraic, is to cancel out common factors. For example, to simplify 10 over 15, you find the biggest common factor, which is 5, and divide the top and bottom by it to get 2 over 3. With algebraic fractions, we do the same thing, but first we need to find the factors by factorising.

Imagine you have the fraction '3x plus 6' all over 'x plus 2'. To simplify it, you first factorise the numerator. '3x plus 6' becomes '3 times, open bracket, x plus 2, close bracket'. Now the whole fraction is '3 times (x plus 2)' all over '(x plus 2)'. You can see that the bracket '(x plus 2)' is a common factor on the top and bottom.