Adding Algebraic Fractions

Addition (and subtraction) of algebraic fractions proceeds in exactly the same manner as for numerical fractions.

Example

Write the following sum as a single fraction in its simplest form.

Solution

The least common multiple of the denominators is ( x + 1)( x + 2) . Thus

Exercise

Evaluate each of the following fractions.

(a)

(b)

Solution

(a) The least common multiple of the denominators is yz . Thus

(b) The least common multiple of the denominators of the two fractions in this case is 6 . Thus

Simplification in this case has shown that the difference of these two fractions is independent of z.

Quiz

Which of the following values of a is needed if

Solution

Writing all the fractions with a common denominator

so that ( a + 2) x + (2 a + 1) = 4 x + 5. This gives two equations

a + 2 = 4 coeffcients of x

2 a + 1 = 5 constant coeffcients

The solution is a = 2.