Substitution method, let m= 1/x, n= 1/y, in fact, you can use it directly when you are skilled, just regard some items as a whole.

For example, the equation x 2+ 1/x 2+2x+2/x-3 = 0 is actually (x+1/x+3) (x+1/x-1) = 0.

So x+ 1/x-3 = 0, x 2-3x+ 1 = 0, x = (3 √ 5)/2.