Don't read the attached file unless you want the answer!
It's a few decades since I thought about things like this but I do remember being unhappy with such problems!
The solution I provided follows a trial and error method whereby you have to make intelligent guesses to arrive at the right answer, i.e. to 'figure it out'! I was reasonably good at doing this but I always thought it was not a good method because I there must be some equations for which I would never be able to work through all the right combinations of possible factors. Just imagine having decimals in such equations!
Well. maths teachers while being very good at getting people through exams, generally avoid dealing with 'real world' problems...the sort that I always knew were out there and that I wouldn't be able to solve by trial and error. Luckily, the people who write exam questions are in on this conspiracy so they make sure that 'everything works out okay'! That's why I was able to guess that the denominator was probably a factor of the numerator.
In the real world: spend a few minutes trying to figure out a solution and if you don't look like getting any where then use the cubic equation formula that I supplied as a link in the attached file.
Similar formulae exist for quartic and quintic equations but, as I recall, not for higher powers.
