Simplify, add and subtract fractions with x in them, and solve equations with algebraic fractions that lead to a quadratic.
What you will learn
- Simplify an algebraic fraction by factorising the top and the bottom
- Add and subtract algebraic fractions over a common denominator
- Solve an equation with algebraic fractions that leads to a quadratic
Cancel factors, never terms
An algebraic fraction simplifies the way 6/8 does: divide the top and the bottom by a common factor.
So factorise both first, then cancel a whole bracket that is on the top and the bottom.
- (x² + 5x + 6) ÷ (x² − 4)
- top: (x + 2)(x + 3)
- bottom: (x + 2)(x − 2), a difference of two squares
- cancel (x + 2)
- = (x + 3)/(x − 2)
(x + 6)/(x + 3) is not 2. The 6 and the 3 are terms, not factors of the whole top and bottom, so nothing cancels. (2x + 6)/(x + 3) is 2, because 2x + 6 = 2(x + 3).
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Cancel factors, never terms
- Adding and subtracting
- Equations with algebraic fractions
7 practice questions, marked as you go; about 30 minutes in all.
In this unit: Quadratics
Expand and factorise quadratics, solve them by factorising, the formula and completing the square, and read roots and turning points from graphs.