PEAZIT Aha card
Go straight to resources ↓Rational expressions: cancel factors, not terms
Cancelling divides the entire numerator and denominator by the same nonzero factor. Factor first, cancel second.
| Expression | Meaning |
|---|---|
| (x² − 4)/(x − 2); x ≠ 2 | The original denominator cannot be zero. |
| ((x − 2)(x + 2))/(x − 2) | Factor the difference of squares. |
| x + 2; x ≠ 2 | Cancel the factor, retaining the original restriction. |
One worked example
- (x² − 4)/(x − 2); x ≠ 2The original denominator cannot be zero.
- ((x − 2)(x + 2))/(x − 2)Factor the difference of squares.
- x + 2; x ≠ 2Cancel the factor, retaining the original restriction.
Watch out: For example, (x + 2)/x cannot be changed into 2. Simplification does not restore excluded values.
Goal, prerequisites and card origin
What you will learn: Simplify a rational expression while keeping its restrictions.
What you need first: Factorisation and cancelling fractions.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Cancelling divides the entire numerator and denominator by the same nonzero factor. Factor first, cancel second.