Solving for x is simply when # y = 0, #in the equation you gave, the right hand side can only evaluate to zero if and only if the numerator, #x + 1 = 0#. The denominator cannot equal to 0, as that would produce an undefined result. Thus you solve:
#x + 1 = 0#
#x = -1#
#f(-1) = 0#
#:. x = -1# is a solution that satisfies the equation.