# Algebraic Fractions

Notes on Algebraic Fractions

- Created by: Natasha Naeem
- Created on: 10-06-11 13:55

First 219 words of the document:

Additional Mathematics

Algebra: Techniques

Section 2: Algebraic fractions

Notes and Examples

These notes contain subsections on

Cancelling algebraic fractions

Adding and subtracting algebraic fractions

Solving equations

Cancelling algebraic fractions

There are other notes on this in the earlier chapter but it is worth bearing in

mind that if something doesn't work with numbers then it will not work when

using letters. Cancelling is a major source of error.

sin x

Try cancelling the `n' in . Do you really think that 6 is the answer?

n

The above was a very silly example but it is often tempting to cancel when

2x 3 5

you shouldn't. E.g. - if we try to cancel x we end up with . But this is

3x 1 2

only true if x = 1, it is untrue for all other values.

There are times when you may need to factorise before you can see if

anything will cancel.

Example 1

Simplify as far as possible:

x2 5x 6 2n 3 2n 2 n 3

(i) (ii)

x 2 x 12 4n 2 9 n5

Solution

x 3 x 2 x 2

(i)

x 4 x 3 x 4

2n 3 2n 3 n 1 n 1

(ii)

2n 3 2n 3 n 5 n 5

© MEI, 24/07/09 1/2

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