Algebraic fractions
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Fractions with letters
- Cancelling
- Simplifying with quadratics
Read the transcript of the teaching part
Last time
Before we start: last time, in Simplifying, expanding and factorising, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Fractions with letters
You can add, subtract, multiply and divide ordinary fractions. Algebraic fractions follow exactly the same rules, with letters in place of some of the numbers. The secret is factorising first: whatever is common can cancel, and whatever is different needs a common denominator.
Cancelling
You can only cancel factors, things that are multiplied. You cannot cancel terms that are added. In six x squared plus nine x over three x, first factorise the top: three x times two x plus three. Now the three x is a common factor on the top and the bottom. It cancels, leaving two x plus three. You cannot cancel the x in x plus two over x. It is a term, not a factor.
Simplifying with quadratics
To simplify x squared minus nine over x squared plus five x plus six, factorise both parts. The top is a difference of two squares: x minus three, times x plus three. The bottom factorises as x plus two, times x plus three. The bracket x plus three is common, so it cancels. The answer is x minus three over x plus two.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Algebraic fractions.
The whole chapter: Algebraic Fractions and Indices.
Chapter 9: Algebraic fractions and indices
- Indices with letters 5 min
- Algebraic fractions 6 min
Also for IGCSE Maths 0580
Which topics come up most in IGCSE Maths 0580 past papers, counted from every paper since 2004.