Some algebraic fractions can be simplified if the numerator and denominator are factorised.
Worked Examples
Simplify
Both the top and bottom of the fraction can be factorised to give
=
The term (x − 3) appears as a factor on both the top and bottom of the fraction so it can be cancelled to give
=
No further simplification is possible.
Simplify
×
First multiply together the fractions to give
× =
The bracket (x2 − 1) can be factorised using the difference of two squares to give
=
Dividing numerator and denominator by common factors gives:
=
No further simplification is possible.
Simplify
÷
Recall from working with fractions that
÷ = × .
So
| ÷ | = × |
| = | |
| = | |
| = |
Simplify
+
Algebraic fractions are added in the same way as ordinary fractions, by using the lowest common denominator. In this case it will be (x + 2)(x + 1).
| + | = + |
| = | |
| = | |
| = |
No further simplification is possible.
Exercises
