Question

help!!! questions from quadratic equations prove----
a/x-a + b/x-a=2c/x-c

Answer 1

a / (x - a) + b / (x - b) = 2c / (x - c)
=> [a(x - b) + b (x - a)] / (x - a) (x - b) = 2c / (x - c)
=> [(a + b) x - 2ab] (x - c) = 2c [x^2 - (a + b)x + ab]
=> (a + b) x^2 - [2ab + c(a + b)]x + 2abc = 2cx^2 - 2c(a + b)x + 2abc
=> (a + b - 2c) x^2 = (2ab + ac + bc - 2ca - 2bc) x
=> (a + b - 2c) x^2 = (2ab - ca - bc) x
=> x = 0
or x = (2ab - ca - bc) / (a + b - 2c)