(3x^2+2)/(x^2-4)-(9x-x^2)/(x^2-4)

Your problem:

(3x^2+2)/(x^2-4)-(9x-x^2)/(x^2-4)

Since the denominator is the same, just subtract the numerator:

(3x^2 + 2 - 9x + x^2)/(x^2 - 4) -->remember to use the distributive property with the negative over the terms in the numerator of the second fraction.

Combine like terms:
(4x^2 - 9x + 2)/(x^2 - 4)

Can we factor to reduce this fraction? Yes.

(4x - 1)(x - 2)/(x + 2)(x - 2)

Can you take it from here to reduce this fraction? (Hint: cancel out the same factors in both the numerator and denominator to reduce.)

I hope this will help.

thank you sooo much. now I know what I did wrong. First I got 2x^2 instead of 4x^2 and then I couldn't manage tpfactor because I didn't see were the nine would fit in. Thanks you for the help!