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?
Division by zero is undefined.
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, it means that the solution you found is not valid.
When a denominator becomes zero, the rational expression becomes undefined. This is because division by zero is undefined in mathematics. So, if one of the denominators becomes zero, the expression as a whole cannot be evaluated.
To avoid this situation, you should always check for any potential values of the variable(s) that would make the denominators equal to zero. These values are called "non-permissible" or "excluded" values. When you find such values, you must exclude them from your solution set.
To determine the non-permissible values, set each denominator equal to zero and solve the resulting equation(s). Any solution(s) you obtain should be excluded from the domain of the variable(s) in order to keep the rational expression well-defined.
By doing so, you can ensure that the solution you find satisfies all the conditions and doesn't make any of the denominators equal to zero.