(A Level) Partial fractions

Learning objectives

Choose the correct partial-fraction form for denominators of the types (ax + b)(cx + d)(ex + f), (ax + b)(cx + d)² and (ax + b)(cx² + d)

Find the unknown constants by substituting convenient values of x, by equating coefficients, or by a mixture of both

Decompose an improper fraction whose numerator has the same degree as its denominator, either by dividing first or by including a constant term in the partial-fraction form

Use a partial-fraction decomposition as the first step in integrating a rational function, expanding it as a binomial series or solving a differential equation