Question 3 - A-Level Maths

Exam Board	AQA
Module	C4 (Core Mathematics 4)
Year	2010
Session	June
Topic	Partial Fractions
Type	Partial fractions with algebraic division first

1. Express \(\frac { 7 x - 3 } { ( x + 1 ) ( 3 x - 2 ) }\) in the form \(\frac { A } { x + 1 } + \frac { B } { 3 x - 2 }\).
2. Hence find \(\int \frac { 7 x - 3 } { ( x + 1 ) ( 3 x - 2 ) } \mathrm { d } x\).
Express \(\frac { 6 x ^ { 2 } + x + 2 } { 2 x ^ { 2 } - x + 1 }\) in the form \(P + \frac { Q x + R } { 2 x ^ { 2 } - x + 1 }\).