1/x + 1/y = 7/12 and xy = 12 therefore for xy = 12 make y subject of the formula ; y = 12/x
Solve by elimination 1/x + 1/(12/x) = 7/12
1/x + x/12 = 7/12 NB: 1/(12/x) simplified becomes x/12
multiply each by 12x or use 12x as a factor
(12x x 1/x) + (12x x x/12) = (12x x 7/12)
12 + x^2 = 7x Rearrange to make zero subject of the formula
x^2 - 7x + 12 = 0 then factorise
(x -3) (x -4) = 0
(x-3) =0 and (x -4) =0
x = 3 and x = 4