Subtract. \[ \frac{3}{x^{2}-3 x+2}-\frac{2}{x^{2}-4 x+4} \] \[ \frac{3}{x^{2}-3 x+2}-\frac{2}{x^{2}-4 x+4}= \] (Simplify your answer. Type your answer in factored form.)

Step 1 ：The problem is asking to subtract two fractions. To subtract fractions, we need to have a common denominator. The denominators of the two fractions are two different quadratic expressions.

Step 2 ：We can factorize these expressions to find the common denominator. The first denominator \(x^{2}-3 x+2\) can be factored into \((x-1)(x-2)\) and the second denominator \(x^{2}-4 x+4\) can be factored into \((x-2)^2\).

Step 3 ：The common denominator would be the product of all distinct factors, which is \((x-1)(x-2)^2\).

Step 4 ：We can then rewrite each fraction with the common denominator and subtract the numerators.

Step 5 ：Finally, we simplify the result if possible. The simplified form of the expression \(\frac{3}{x^{2}-3 x+2}-\frac{2}{x^{2}-4 x+4}\) is \(\frac{-2(x - 1)^2 + 3(x^2 - 4x + 4)^2}{(x - 1)(x^2 - 4x + 4)}\)

Step 6 ：\(\boxed{\frac{-2(x - 1)^2 + 3(x^2 - 4x + 4)^2}{(x - 1)(x^2 - 4x + 4)}}\) is the final answer.