1. The problem is to factorise the numerator of a given expression. 2. To factorise a numerator, we look for common factors or use methods like grouping, difference of squares, or quadratic factorisation. 3. Suppose the numerator is a polynomial like $ax^2 + bx + c$. 4. We use the quadratic formula or factor by finding two numbers that multiply to $ac$ and add to $b$. 5. For example, if the numerator is $x^2 + 5x + 6$, we find factors of 6 that add to 5, which are 2 and 3. 6. So, $x^2 + 5x + 6 = (x + 2)(x + 3)$. 7. If the numerator has a common factor, factor it out first, e.g., $2x^2 + 4x = 2x(x + 2)$. 8. Always check your factorisation by expanding back to the original expression.