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 · d - b · c . This is almost exactly the same as the pattern of cross-multiplying . The only difference is that because the fractions are subtracted, a minus sign now joins the a · d to the b · 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 · x + 6. Note that the “ - ” sign in the numerator applies to both the 3 · x and the +6, giving - 3 · x - 6 in the numerator, not - 3 · x + 6.

As in the previous example, note that the “ - ” that appears in from of the x · ( x + 1) in the numerator applies to both the xand the x that are generated when x · ( x + 1) is multiplied out. This gives the - x - x that appears in the numerator, not - x+ x .