Find the roots by factorisation method

Question

{a/(x-a)} + {b/(x-b)} = {2c/(x-c)}

Answer 1

Multiplying both sides with(x-a)(x-b)(x-c) we get:

 

 a(x-b)(x-c) + b (x-a)(x-c) = 2c(x-a)(x-b)

a(x^2 -bx -cx +bc) + b(x^2 -ax -cx +ac) = 2c(X^2 -xa -bx +ab)

 

=>(a+b)x^2 -(ac+ab+ab+bc)x + 2abc =2cx^2 -(2ac+2bc)x + 2abc

=>(a+b -2c)x^2 -(2ab -ac-bc)x = 0

=>x((a+b -2c)x -(2ab-ac-bc)) = 0

x = 0 or (a+b-2c)x -(2ab -ac -bc) = 0

 

=> x = 0 , x = (2ab-ac -bc)/(a+b -2c)