What happens if you are checking a solution for the rational expression and find that it makes one of the denominators in the expression equal to zero?
It means that the expression is undefined for that particular solution.
e.g.
suppose we have the expression (x+5)/(x^ - 4) and we are given that x = 2
we could get
7/0 , which is undefined
so we would state the expression as
(x+5)/(x^2 - 4) , x ≠ ± 2
If you are checking a solution for a rational expression and find that it makes one of the denominators in the expression equal to zero, that indicates a potential issue. When a denominator becomes zero, it results in division by zero, which is undefined in mathematics.
To handle this situation, the expression is said to have a "restriction" or an "excluded value" at the values that make the denominator zero. These values are not valid solutions for the given rational expression because they lead to mathematical inconsistencies.
So, if you encounter a solution that makes a denominator zero, you need to exclude that value from the solution set. This means that the solution is not valid and is not a solution to the rational expression.
To find the values that make the denominator zero, set each denominator equal to zero and solve for the variable. The resulting values will be the excluded values or restrictions.