If the roots of the equation ax−a+bx−b=1  are equal numerically and are opposite in sign then

The given equation is ax−a+bx−b=1 Given that the roots are equal and opposite in sign∴  the sum of the roots is 0.The given equation can be written as a(x−b)+b(x−a)=  (x−a)(x−b) ⇒ax+bx−2ab=x2−(a+b)x+ab  ⇒x2−2  (a+b)x+3ab=0 ⇒     sum of the roots =  2(a+b)1=0.  ∴a+b=0