(a/x-b) + (b/x-a) =2 using quadratic formula
a/(x - b) + b/(x - a) = 2
a(x - a) + b(x - b) = 2(x - a)(x - b)
x(a + b) - (a^2 + b^2) = 2(x^2 - (a+b)x + ab)
2x^2 - 3(a + b)x + (a + b)^2 = 0
Quadratic formula is: x = {-B +/sqrt(B^2 - 4AC)}/(2A), where A = 2, B = -3(a + b), C = (a + b)^2
So then,
x = {3(a + b) +/- sqrt(9(a + b)^2 - 4*2*(a + b)^2)} / (2*2)
x = {3(a + b) +/- sqrt((a + b)^2)} / (4)
x = (a + b){3 +/- 1)} / (4)
x = (a + b){1 , 1/2)}
Answer: x = (a + b), x = (a + b)/2