Another Hard Simplifying question?

Question

one more that I need some help with please, this needs to be simplified

{(x-1)/(x^2-9)}+{(2x-3)/(x^2-4x+3)}

Answer 1

{(x-1)/(x^2-9)}+{(2x-3)/(x^2-4x+3)}

={(x-1)/ [(x-3)(x+3)]} +  {(2x-3)/[(x-3)(x-1)]}: multiply by Mr. One

=[(x-1)/(x-1)] * {(x-1)/ [(x-3)(x+3)]} +  {(2x-3)/[(x-3)(x-1)]} * [(x+3)/(x+3)]

={(x-1)(x-1)/ [(x-3)(x+3)(x-1)]}  +  {(2x-3)/[(x-3)(x+3)(x-1)]}

=(x-1)(x-1)(2x-3)/[(x-3)(x+3)(x-1)]

=(x-1)(2x-3)/[(x-3)(x+3)]