Express x2−5x+16x3−7x2+15x−9\displaystyle \frac{x^2-5x+16}{x^3-7x^2+15x-9}x3−7x2+15x−9x2−5x+16 in the form A(x−1)+B(x−3)+C(x−3)2\displaystyle \frac{A}{(x-1)} + \frac{B}{(x-3)} + \frac{C}{(x-3)^2}(x−1)A+(x−3)B+(x−3)2C, giving the values of AAA, B B\,B and C C\,C exactly.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.