An algebraic fraction can be simplified by cancelling a factor that is common to the whole top and the whole bottom. To simplify (4x + 20)/4, factorise the top: 4(x + 5)/4 = x + 5.
You can only cancel factors, never single terms joined by + or −. In (2x² − 2x)/(2x), factorise the top to 2x(x − 1), then cancel the 2x to get x − 1. Factorise the top and the bottom fully before you cancel.
Worked example
Simplify (12x + 3)/(4x + 1)
- Factorise the top: 3(4x + 1).
- Cancel the common factor (4x + 1).
Answer:3
Key words
- algebraic fraction
- a fraction with letters
- cancel
- divide top and bottom by the same factor
- factor
- something multiplied, like (x + 5)
Practise this
New questions every time.
Common Core-referenced: HSA-SSE.A.2