Please send the solution to the problem given in the attachment.

When you cancelled x-3 from numerator and denominator ,you assumed that x is not equal to 3 so your domain will be R\{3} in second case also. So Answer will be same in both cases.

Any doubt then you can ask.

Thing is you can't cancel if x-3 =0 , this Operation is not valid until x-3 is non zero. If I can like zero quantity then I can prove 1=2