Rational expressionsEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

What is a rational expression?
What can you cancel in a rational expression?
Simplify \frac{x^2-9}{x^2+x-6}.
Factorise x^2-a^2.
Factorise x^3+8.
Simplify \frac{x^3+8}{x^2-4}.
How do you divide by a rational expression?
How do you add \frac{1}{x+1}+\frac{2}{x-1}?
Write \frac{x-3}{x-2} as a constant plus a fraction.
Write \frac{x^2-2x+4}{x-2} as a polynomial plus a fraction.
Where is \frac{x^2-9}{x^2+x-6} undefined?
Why check solutions in the original expression?

Exam questions on Rational expressions

The expression $\frac{x^2-9}{x^2+x-6}$ is defined for all real $x$ except where the denominator is zero.
Hence write $\frac{x^2-9}{x^2+x-6}$ in the form $A+\frac{B}{x-2}$ , where $A$ and $B$ are constants.2 marks
The expression $\frac{x^3+8}{x^2-4}$ is considered for values of $x$ where it is defined.
Hence write $\frac{x^3+8}{x^2-4}$ in the form $x+\frac{k}{x-2}$ , where $k$ is a constant.2 marks
The function $f(x)=\frac{3x^2+x-2}{2x^2-x-3}$ is defined for all real $x$ except where its denominator is zero.
Simplify $f(x)$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).