Partial fractionsAQA A-Level Maths: Mind map

Exam questions on Partial fractions

1. It is given that $\dfrac{7x+1}{(x-1)(x+2)}\equiv\dfrac{A}{x-1}+\dfrac{B}{x+2}$ for all $x\neq1,-2$, where $A$ and $B$ are constants.
   Verify that the partial fractions you found for $A$ and $B$ are correct by substituting $x=0$ into both sides of the identity.2 marks
2. It is given that $\dfrac{5x+3}{(x+1)^2}\equiv\dfrac{P}{x+1}+\dfrac{Q}{(x+1)^2}$ for all $x\neq-1$, where $P$ and $Q$ are constants.
   Use the partial fractions to evaluate $\dfrac{5x+3}{(x+1)^2}$ when $x=1$.2 marks
3. Let $\mathrm{f}(x)=\dfrac{4x+9}{(x+2)(x+3)}$ and $\mathrm{g}(x)=\dfrac{5x+4}{(x-1)(x+2)^2}$, defined for values of $x$ where the denominators are non-zero.
   Express $\mathrm{f}(x)$ in partial fractions.3 marks