Solve this (3/x+1)*(1/x-1)=5/4
(3/x+1)*(1/x-1)=5/4 -- multiply out the brackets
3/x^2 - 3/x + 1/x - 1 = 5/4
3/x^2 - 2/x = 9/4 -- multiply both sides by x^2
3 - 2x = 9x^2/4
12 - 8x = 9x^2
9x^2 + 8x - 12 = 0 -- use the quadratic formula to solve this
settiing a = 9, b = 8, c = -12,
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
x = (-8 +/- sqrt(64 + 432)) / (18)
x = (-8 +/- sqrt(496)) / 18
x = (-8 +/- 4.sqrt(31)) / 18
x = -4/9 + (2/9)sqrt(31), x = -4/9 - (2/9)sqrt(31)