Algebraic Fractions

Notes on Algebraic Fractions

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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?
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
x 3 x 2 x 2
x 4 x 3 x 4
2n 3 2n 3 n 1 n 1
2n 3 2n 3 n 5 n 5
© MEI, 24/07/09 1/2

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AM Algebra techniques 2 Notes and Examples
Adding or subtracting algebraic fractions
When adding or subtracting, a common denominator is required. The lowest
common denominator is best as it saves work later.…read more


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