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2.5 Simplifying algebraic fractions

2.5 Simplifying algebraic fractions

In this section you will … Key word

• simplify algebraic fractions. algebraic fraction

An algebraic fraction is a fraction that contains an unknown variable, or letter. For example,

x y 8 2a 5 x 1
, , , and are all algebraic fractions. You can write the fraction (say ‘x over 4’) as x (say
4 2 z 3 4b 4 4
2a
2
‘one-quarter of x’). You can write the fraction (say ‘2a over 3’) as a (say ‘two-thirds of a’).
3 3
To add and subtract algebraic fractions, use the same method as for normal fractions.
• If the denominators are the same, simply add or subtract the numerators.
• If the denominators are different, write the fractions as equivalent fractions with the same
denominator, then add or subtract the numerators.
• Cancel your answer to its simplest form.

Worked example 2.5

Simplify these expressions.
x
a x + b 4 − 5 c n + 2
6 6 y 2y 5 3 p

Answer
a x + x = x + x The denominators are the same, so add the numerators.
6 6 6
= 2 x Cancel the fraction to its simplest form.
6
x
1x
= x Write as .
3 3 3
8
4
5
8
5
b 4 − 2y = 2y − 2y The denominators are different, so change to .
2y
y
y
= 8 − 5 The denominators are now the same, so subtract the numerators.
2y
= 3 3 cannot be simplified, so leave it as it is.
2y 2y

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