The nonzero integer solution of the equation "1 / x plus 1 / y minus 1 / 2 of xy = 3 / 4" is_____

The nonzero integer solution of the equation "1 / x plus 1 / y minus 1 / 2 of xy = 3 / 4" is_____

（1/x）+（1/y）-（1/x²y²）=3/4
General score, (XY & # 178; X & # 178; Y & # 178;) + (X & # 178; Y / X & # 178; Y & # 178;) - (1 / X & # 178; Y & # 178;) = 3 / 4
Multiply both sides by X & # 178; Y & # 178; to get XY & # 178; + X & # 178; Y-1 = 3 / 4 * X & # 178; Y & # 178;
Multiply 4x and 178; y + 4xy and 178; - 4 = 3x and 178; y and 178;
We get 4xy (x + y) - 3xy * xy = 4
By raising the common factor, XY {4 (x + y) - 3xy} = 4
=xy（4x+4y-3xy）=4
Because X and y are all nonzero integers
therefore
xy=1,2,4,-1,-2,-4,
① When xy = 1, x = 1, y = 1, or x = - 1, y = - 1,
② When xy = 2, x = 1, y = 2, or x = - 1, y = - 2,
③ When xy = 4, x = 1, y = 4, or x = 2 = y, or x = - 1, y = - 4, or x = y = - 2
and so on,.
Then substitute the original formula to get x = y = 2