Rational Expressions and Non-Permissible Values:
A rational expression is the ratio of two polynomials:
Non-permissible values are values of the variable(s) that make the denominator of a rational expression equal to zero. In order to find the non-permissible values of a rational expression one has to set the denominator equal to zero and solve it for the variable. Below, we look at few examples on how to find non-permissible values.
Example: Find non-permissible values of .
We set the denominator equal to zero:
Now, we solve for x:
Therefore, are the non-permissible values.
WARNING!! Do not use the simplified form of a rational expression to find its non-permissible values. When we simplify a rational expression, we might lose some of its non-permissible values.
Example: Find non-permissible values of.
To find the non-permissible values we have to set the denominator equal to zero:
Since we have the product of two terms here, we have to set each term equal to zero and solve for x:
Therefore, the non-permissible values are
Attention! If we simplify the expression, we get
which has no non-permissible values. Therefore, we have to find non-permissible values before we simplify an expression.