Solution of a equation . 
Solve the equation:
  $\frac{a}{ax-1}$+$\frac{b}{bx-1}$=$a+b$

It is my problem.I simply evaluate the equation and I found $ab(a+b)x^2-[(a+b)^2+2ab]x+2(a+b)=0$.I use Sridhar Achharya's theorem but it became complicate . Somebody please help me to solve the equation.

$ab(a+b)x^2-[(a+b)^2+2ab]x+2(a+b)=0$
$(abx-a-b)(ax+bx-2)=0$
