Rút gọn biểu thức

To simplify the expression, we need to combine like terms and factor where possible.

Given expression: 3a + 2/(x^2 - 2x + 1) - 6/(x^2 - 1) - 3x + 6/(x^2 - 2x + 3)

First, let's factor the denominators of the fractions:

x^2 - 2x + 1 = (x - 1)(x - 1) = (x - 1)^2
x^2 - 1 = (x + 1)(x - 1)
x^2 - 2x + 3 = (x - 1)(x - 3)

Now, rewrite the expression with the factored denominators:

3a + 2/(x - 1)^2 - 6/(x + 1)(x - 1) - 3x + 6/(x - 1)(x - 3)

Next, find a common denominator for the fractions:

Common denominator = (x - 1)^2(x + 1)(x - 3)

Now, rewrite each fraction with the common denominator:

(3a(x - 1)^2(x + 1)(x - 3) + 2(x + 1)(x - 3) - 6(x - 1)^2(x - 3) - 3x(x - 1)^2(x + 1) + 6(x - 1)^2(x + 1))/(x - 1)^2(x + 1)(x - 3)

Simplify the expression further if needed.