Simplifying rational expressionsEdexcel International A Level Maths: Mind map

Exam questions on Simplifying rational expressions

1. Let $f(x)=\dfrac{x^2-9}{x^2+x-12}$.
   Solve $f(x)=2$.2 marks
2. Let $h(x)=\dfrac{x^3+1}{x^2-1}$.
   Hence find constants $a$, $b$ and $c$ such that $h(x)\equiv ax+b+\dfrac{c}{x-1}$ for $x\neq\pm1$.2 marks
3. Let $F(x)=\dfrac{2x^3-3x^2-11x+6}{x^2-x-6}$, where $x\in\mathbb{R}$, $x\neq 3$, $x\neq -2$.
   Simplify $F(x)$ fully, showing your factorisation of the numerator.3 marks