Final answer:
To subtract and simplify the given expression, find a common denominator for the fractions and then simplify the expression.
Step-by-step explanation:
To subtract and simplify the given expression, you need to find a common denominator for the fractions. The denominators are x²-4x+3 and x-3. The common denominator is (x-3)(x+1).
Now, multiply the first fraction by (x+1)/(x+1) and the second fraction by (x²-4x+3)/(x²-4x+3) to obtain a common denominator for both fractions.
The simplified expression is [(6x+5)(x+1) - 6(x²-4x+3)] / (x-3)(x+1).