1/x - 2/(x-3) = 4
multiply each side by x*(x-3)
x*(x-3)(1/x - 2/(x-3)) = 4*x*(x-3)
distribute
x*(x-3)(1/x) - 2/(x-3))x*(x-3) = 4*x*(x-3)
cancel
(x-3) - 2*x = 4x(x-3)
distribute
x-3-2x = 4x^2-12x
combine like terms
-x-3 = 4x^2 -12x
add x+3 to each side
0 = 4x^2 -12x+x+3
0 = 4x^2 -11x+3
using the quadratic formula
x= 11/8 - sqrt (73)/8
x=11/8 + sqrt (73)/8