Recall that:
An expression that is written in the form of a fraction (or ratio) is
called a rational expression.
Simplification of Rational Expressions
In general:
From this, we can say that:
Only factors can be cancelled.
This suggests that the division by 3 is not permissible. In other words,
we can not cancel 3 as it is not a factor
of the numerator.
Example 1
Solution:
Often, we set out the solution as follows:
Example 2
Solution:
We often use the following steps to simplify algebraic fractions:
- Factorise the numerator and denominator.
- Cancel the factors
that are common to the numerator and denominator.
This process is called reducing the fraction to its lowest terms.
Example 3
Solution:
Example 4
Solution:
Remember:
Factorise and then cancel the common
factors.
Example 5
Solution:
Example 6
Solution:
Key Terms
rational expression |
