Unit 5 sec
4.2 Algebraic fraction
20
January 2016
01:44
Similarly, the expression
(8a + 3) ÷ (2a)
can be written in fraction notation as
8a + 3
2a.
The brackets can be omitted because the fraction notation
makes it clear
that the whole of 8a + 3 is divided by 2a.
The expressions above and below the line in an algebraic
fraction are called the numerator and denominator,
respectively, just as
they are for ordinary fractions.
(8a + 3) ÷ (2a)
should be written as
8a + 3
2a
, not
8a + 3
2a
Try not to use division signs in expressions, or whenever
you carry out algebraic manipulation, from now on; use fraction notation
instead.
However, occasionally it’s useful to use division signs in
algebraic expressions, just as occasionally it’s useful to use multiplication
signs.
As with multiplying out brackets, this technique doesn’t
necessarily simplify an expression; it just gives a different way of writing
it. It applies to algebraic fractions where there’s more than one term in the numerator,
such as
2a − 5b +
c
3d
Since dividing by something is the same as multiplying by
its reciprocal,
you can write this expression as
1
3d
(2a − 5b + c).
You can then multiply out the brackets to give
2a
3d
− 5b
3d
+
c
3d
If you compare expressions (6) and (7), you can see that the
overall effect is that each term on the numerator has been individually divided
by the denominator. This is called expanding the algebraic
fraction.
Once an algebraic fraction has been expanded, it may be
possible to simplify some of the resulting terms, as illustrated in the next
example
Example 15 Expanding an algebraic fraction
Expand the algebraic fraction
10x + x2
– 8
x
.
Solution
10x + x2
– 8 = 10x + x² − 8 = 10 + x − 8
X x x
x x
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