Subtracting Fractions
Expressed in symbols, the rule for subtracting one fraction
from another is as follows:
Let’s break this down to see everything that is expressed
in this rule. The numerator of the sum is a Â· d  b Â· c . This
is almost exactly the same as the pattern of crossmultiplying .
The only difference is that because the fractions are subtracted,
a minus sign now joins the a Â· d to the b Â· c .
To get the denominator of the sum, you just multiply the two
denominators ( b and d ) together.
Example
Work out each of the following differences of fractions.
Solution
In the numerator, the “3” multiplies the entire
quantity ( x + 2) to give 3 Â· x + 6. Note that the “ 
” sign in the numerator applies to both the 3 Â· x and the
+6, giving  3 Â· x  6 in the numerator, not  3 Â· x + 6.
As in the previous example, note that the “  ” that
appears in from of the x Â· ( x + 1) in the numerator applies to
both the xand the x that are generated when x Â· ( x
+ 1) is multiplied out. This gives the  x
 x that appears in the numerator, not  x+
x .
