My solution is on the file, but here I will help explain my thought process.
The initial equation is a clue to help us solve the problem. By rearranging the equation and taking all of the terms onto one side, we have an expression that is less than (or greater than - if you rearrange to the opposite side of the equation that I did) zero. Furthermore, if we have two terms that are greater than zero all we have to do is somehow make one of them less than zero and find the product, which we know will also be less than zero. This will then match what we have done to the equation and then we can try and factorise.
As x and y are both between one and zero, they are symmetrical and so we can choose either variable. I chose to subtract 1 from x, making (x-1) negative. I know the equation has a 1 and an xy in it so I need an expression with a 1 and a y in it. Also, I need an expression that it greater than zero, as explained above. Therefore, I chose 1-y. Now by expanding (x-1)(1-y) the rest of the solution is obvious, and is described in the file attached.