Help with this complex fraction please...

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

LCM is (a-1) (a+2) (a+3) right? then i get stuck

To simplify the given complex fraction, you can start by finding the common denominator for both terms in the numerator. However, the LCM you have mentioned, (a-1)(a+2)(a+3), is not the correct common denominator.

To find the correct common denominator, you need to consider the individual denominators first, which are (a^2 + a - 2) and (a^2 + 2a - 3). Let's factorize both denominators individually:

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

Now, you can see that the common denominator is (a + 2)(a - 1)(a + 3). Let's rewrite the complex fraction using this common denominator for both terms:

((a+2) / (a + 2)(a - 1)(a + 3)) - ((3a+1) / (a + 2)(a - 1)(a + 3))

Now, you can combine the terms by subtracting them:

((a+2) - (3a+1)) / (a + 2)(a - 1)(a + 3)

Expanding the numerator:

(a + 2 - 3a - 1) / (a + 2)(a - 1)(a + 3)

Simplifying the numerator:

(-2a + 1) / (a + 2)(a - 1)(a + 3)

So, the simplified complex fraction is (-2a + 1) / (a + 2)(a - 1)(a + 3).