[tex]\frac{a}{x+a} + \frac{b}{x-b} = \frac{a+b}{x+c}\\\frac{a(x-b) + b(x+a)}{(x+a)(x-b)} = \frac{a+b}{x+c} \\\frac{x(a+b)}{(x+a)(x+b)} = \frac{a+b}{x+c}\\x(x+c) - (x+a)(x+b) = 0\\x(c -b -a) = ab\\x = \frac{ab}{c-b-a}[/tex]
