Cambridge International Mathematics

340 Algebraic fractions (Chapter 16)

The same principle can be applied to algebraic fractions:

If the numerator and denominator of an algebraic fraction are both written in factored form and common

factors are found, we can simplify bycancelling the common factors.

For example,

4 ab

2 a

=

2 £ 2 £a£b

2 £a

ffully factorisedg

=

2 b

1

fafter cancellationg

=2b

For algebraic fractions, check both the numerator and denominator to see if they

can be expressed as the product of factors, then look for common factors which

can be cancelled.

ILLEGAL CANCELLATION

Take care with fractions such as

a+3

3

:

The expression in the numerator, a+3, cannotbe written as the product of

factors other than 1 £(a+3):aand 3 aretermsof the expression, not factors.

A typicalerrorinillegal cancellationis:

a+3

3

=

a+1

1

=a+1.

You can check that this cancellation of terms is incorrect by substituting a value fora.

For example, if a=3then LHS=

a+3

3

=

3+3

3

=2, whereas RHS=a+1=4.

Example 1 Self Tutor

Simplify: a

2 x^2

4 x

b

6 xy

3 x^3

c

x+y

x

a

2 x^2

4 x

=

2 £x£x

4 £x

=

x

2

b

6 xy

3 x^3

=

6 £x£y

3 £x£x£x

=

2 y

x^2

c

x+y

x

cannot be simplified

as x+y is a sum,

not a product.

When cancelling in

algebraic fractions,

only factors can be

cancelled, not terms.

11

11

1

1

2

11

1

2 1

(^11)
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