To solve the system of equations:

1) xy = 12
2) 3/x - 1/y = 5/12

We can start by rearranging the second equation to isolate y:

3/x - 1/y = 5/12
Multiply through by xy (which equals 12):

3y - x = 5
3y = x + 5
y = (x + 5) / 3

Now, substitute this y value into the first equation:

x[(x + 5)/3] = 12
x(x + 5) = 36
Expanding and rearranging:

x^2 + 5x - 36 = 0
(x + 9)(x - 4) = 0

This gives us two possible values for x: x = -9 or x = 4

Substitute these back into the equation for y to find the corresponding values:

1) For x = -9:
y = (-9 + 5) / 3
y = -4 / 3

2) For x = 4:
y = (4 + 5) / 3
y = 9 / 3
y = 3

Therefore, the solutions to the system of equations are: (-9, -4/3) and (4, 3)