Question 109173
[(x+4)/(x^2-3x+2)] - [ 5 /( x^2-4x+3)]  = [(x-4)/(x^2-5x+6)]

Factor where you can to get:
 
[(x+4)/(x-2)(x-1))] - [ 5 /( x-1)(x-3))]  = [(x-4)/(x-6)(x+1)]

Multiply thru by (x-2)(x-1)(x-3)(x-6)(x+1) to get a mess:

[(x+4)(x-3)(x-6)(x+1)] -[5(x-2)(x-6)(x+1)] = (x-4)(x-2)(x-1)(x_3)

I'll let you multiply out this mess and simplify each term.
Personally, I think this kind of problem is nothing but busy
work.
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Cheers,
Stan H.