It means that the answer can be written as a fraction using whole numbers (integers) i.e. 3/4 or 1/8 or 5 (which is identical to 5/1 and hence rational)
If one of the denominators becomes equal to zero when checking a solution for a rational expression, it means that the expression is undefined at that point. This is because division by zero is not defined in mathematics. Therefore, the solution you found is not valid for that rational expression.
you've done something wrong
Presumably you'll arrive at the wrong solution.
Then it is not a solution of the original equation. It is quite common, when solving equations involving radicals, or even when solving equations with fractions, that "extraneous" solutions are added in the converted equation - additional solutions that are not solutions of the original equation. For example, when you multiply both sides of an equation by a factor (x-1), this is valid EXCEPT for the case that x = 1. Therefore, in this example, if x = 1 is a solution of the transformed equation, it may not be a solution to the original equation.
The answer is a rational number.
The product is a rational number.
The product of two rational numbers is always a rational number.
The result will also be a rational number.
Such a product is always irrational - unless the rational number happens to be zero.
No. It is not defined if the rational number happens to be 0.
When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.
Sh!t happens.