Not factorising before cancelling
"The Hasty Canceller"
The Mistake in Action
Simplify $\frac{x^2 - 9}{x + 3}$
Wrong: "This cannot be simplified because there's no common factor."
Why It Happens
Students look for obvious common factors without recognising that factorising the numerator would reveal a hidden factor.
The Fix
Always check if the numerator or denominator can be factorised.
$x^2 - 9$ is a difference of two squares!
$\frac{x^2 - 9}{x + 3} = \frac{(x+3)(x-3)}{x + 3} = x - 3$
Strategy: Always try to factorise before saying "cannot be simplified".
Spot the Mistake
Can you identify where this student went wrong?
$\frac{x^2 - 9}{x + 3}$
cannot be simplified
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: