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.
