Algebraic fractions
Algebraic fractions (Extended)
- An algebraic fraction has algebra on top or bottom — add/subtract with a common denominator.
- $\dfrac{x}{3} + \dfrac{x-4}{2} = \dfrac{2x + 3(x-4)}{6} = \dfrac{5x - 12}{6}$.
- To simplify a rational expression, factorise top and bottom, then cancel: $\dfrac{x^2 - 2x}{x^2 - 5x + 6} = \dfrac{x(x-2)}{(x-2)(x-3)} = \dfrac{x}{x-3}$.
Practice
Simplify (x² − 2x)/(x² − 5x + 6).
Factorise: x(x−2) / [(x−2)(x−3)], cancel (x−2) → x/(x−3).
Practice
Add x/3 + (x−4)/2 over a common denominator of 6.
2x/6 + 3(x−4)/6 = (2x + 3x − 12)/6 = (5x − 12)/6.
Practice
To divide algebraic fractions, multiply by the reciprocal of the second one.
Division by a fraction is multiplication by its reciprocal, just as with numbers.
You've got it
Key idea
- add/subtract algebraic fractions with a common denominator
- multiply/divide as with ordinary fractions (divide = × the reciprocal)
- simplify by factorising then cancelling common brackets