When asked to simplify a sum, difference or quotient of algebraic fractions, never expand the numerator. Factorise every quadratic into its linear brackets first, then cancel common factors top and bottom before combining terms over a common denominator.
Trigger: a sum, difference or quotient of rational expressions to be simplified.
Instances:
(i) factorise every quadratic expression into linear brackets;
(ii) cancel common linear factors top and bottom to reduce the degree;
(iii) dividing by a fraction is multiplying by its reciprocal, which brings more linear brackets into contact for cancellation.
