Question

$\frac{a}{x - a} + \frac{b}{x - b} = \frac{2c}{x - c}$

Answer 1

weheya..!!!

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

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

=> (ax - ab + bx - ab) / (x - a)(x - b) = 2c/(x - c)

=> (ax + bx - 2ab) / (x - a)(x - b) = 2c/(x - c)

=> (ax + bx - 2ab )(x - c) = 2c(x - a)(x - b)

=> ax² + bx² - 2abx - acx - bcx + 2abc = 2c(x² - bx - ax + ab)

=> ax² + bx² - 2abx - acx - bcx + 2abc = 2cx² - 2bcx - 2acx + 2abc

=> ax² + bx² - 2cx² = - 2bcx - 2acx + 2abc + 2abx + acx + bcx - 2abc

=> x²(a + b + c) = -bcx - acx + 2abx

=> x²(a + b + c) = x( -bc - ax + 2ab)

=> (a + b + c)x² - x(2ab - ac - bc) = 0

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

=> x = 0

AND,

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

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