You can't have answers to algebraic fractions that render the denominator 0 (because then you would have 1/0, which is not defined). In this case, you have 2 solutions that would not work. If x = 7, then the denominator of the first fraction (x-7) would equal 0. For the second fraction, if x = 0, then the denominator (x) would equal 0. Those are the only solutions that would not "be possible" algebraically because they're not in the domain of the function.