About Zeros in the Denominator of Rational Expressions

One thing that you must be careful about when working with rational expressions is that the denominator can never be zero. Division by zero is undefined. So any values for the variables that would make the denominator zero must be excluded from the domain of the expression.

Let me show you what I mean by this. You should carefully study the following examples.

For the following, state the values of the variable that must be excluded from the rational expression:

2x -3/x2-3x-10

Solution: Again, exclude the values for which the denominator, or
x² - 3x - 10 = 0:
x² - 3x -10 = 0
(x - 5)(x +2) = 0
x - 5 = 0 or x + 2= 0
x = 5 or -2
So this means that x = 5 and x = -2.