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Adding algebraic fractions

Algebraic fractions can be added together using the same method that we use for numerical fractions.

The fractions need to be written over a common denominator before they can be added together.

1a

+2b

=b + 2a

abbab

+2aab

=

In general, the rule for adding together algebraic fractions is:

+ =ab

cd

ad + bcbd

How would you complete this calculation: + ?1a

2b

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How would you complete this calculation: + ?

Adding algebraic fractions

We need to write the fractions over a common denominator before we can add them.

3x

y2

3x

+y2

=

=6 + xy

2x

+62x

xy2x

=

+3 × 2x × 2

y × x2 × x

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Adding algebraic fractions

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Addition pyramid

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Subtracting algebraic fractions

Subtracting algebraic fractions uses the same method as is used when dealing with numerical fractions.

We need to write the fractions over a common denominator before we can subtract them.

In general, the rule for subtracting algebraic fractions is:

– =p3

q2

– =2p6

3q6

2p – 3q6

– =ab

cd

ad – bcbd

How would you complete this calculation: – ?p3

q2

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Subtracting algebraic fractions

–(2 + p) × 2q

4 × 2q3 × 42q × 4

=–2 + p

432q

= –2q(2 + p)

8q128q

=2q(2 + p) – 12

8q4

6

=q(2 + p) – 6

4q

How would you complete this calculation: – ?

2 + p4

32q

Remember to cancel both parts of the numerator.

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Subtracting algebraic fractions

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Manipulating algebraic fractions

If two terms are added or subtracted in the numerator, the fraction can be split in two over a common denominator.

a + bc

can be written asbc

ac

+

For example, 1 + 23

=23

13

+

If two terms are added or subtracted in the denominator of a fraction, we cannot split the fraction into two.

For example, 3

1 + 2=

32

31

+

ca + b

cannot be written ascb

ca

+

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Fraction rules