The general term is
So, the second term is
Note that there is certainly a MUCH shorter way doing this. However, for good pedagogy, I worked this expansion out completely for you (so you understand each step). I will assume you know how to compute binomial coefficients (i.e. 6 choose 4).
Find the coefficient of x4 in the expansion of (3x - 1/x)6
We want to expand .
The Binomial Theorem states:
We let:
So,
So, what does the coefficient of look like to you?
-Andy