Partial fractionsEdexcel A-Level Maths: Mind map

Exam questions on Partial fractions

1. $\frac{5x+1}{(x-1)(x+2)}\equiv\frac{A}{x-1}+\frac{B}{x+2}$, where $A$ and $B$ are constants.
   Hence find $\int\frac{5x+1}{(x-1)(x+2)}\,dx$.2 marks
2. $f(x)=\frac{7x+4}{(x+1)(2x-1)}$, $x\neq-1$, $x\neq\frac12$. It is given that $f(x)\equiv\frac{A}{x+1}+\frac{B}{2x-1}$.
   Find the coefficient of $x^2$ in the series expansion of $f(x)$ in ascending powers of $x$, valid for $|x|<\frac12$.2 marks
3. $g(x)=\frac{3x^2+7x+5}{(x+1)(x+2)^2}$, $x>-1$.
   Find the values of the constants $A$, $B$ and $C$ such that $g(x)\equiv\frac{A}{x+1}+\frac{B}{x+2}+\frac{C}{(x+2)^2}$.3 marks