A Traditional Algebra 2 Rational Equation for the Holidays or ...

Solve for x:



Comments:
(1) The traditional procedure is time-consuming but part of the rites of passage for Algebra 2 students. This is the kind of exercise that "trains the brain!"
(2) Note that the form of the equation is a + (1/a) = 2. Does this suggest anything to you?
(3) Would this question be appropriate for SATs? Algebra 2 End of Course Exams?