Question

a/x-a + b/x-a=2c/x-c

Answer 1

given,a/(x-a) + b/(x-b) = 2c/(x-c)
[a(x-b)+b(x-a)]/(x-a)(x-b) = 2c/(x-c)
(x-c)[a(x-b)+b(x-a)] = 2c(x-a)(x-b)

ax2 – 2abx + bx2 - acx + 2abc – bcx = 2cx2 – 2bcx – 2acx + 2abc
ax2+ bx2 - 2cx2 = 2abx – acx – bcx
(a+b-2c)x2 = x(2ab – ac – bc)
(a+b-2c)x2 - x(2ab – ac – bc) = 0
x[(a+b-2c)x - (2ab – ac – bc)] = 0
x = 0 or (a+b-2c)x - (2ab – ac – bc) =0
x = 0 or (a+b-2c)x = (2ab – ac – bc)
x = 0 or x = (2ab – ac – bc) / (a+b-2c)
thus the 2 roots of the given equation are x = 0 and x = (2ab – ac – bc) / (a+b-2c)