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Im having some troubles with this binomial expansion...

Determine the coefficient of x^k, where k is any integer, in the expansion of (2x - 1/x)^2007.

I figured it would just be

C(2007,k) * (2x)^2007-k * (-1/x)^k

= C(2007,k) * (2)^2007-k * x^2007-k * (-1/x)^k

therefore the coefficient would only be the constant terms with no variables

but when i tried it on a smaller scale (ie small exponent), and factored it out, the equation i found doesnt work

i think it is due to the common variable x

anyone kno what to do?