How do I solve with binomial theorem here?

Question

Use the binomial theorem to find the term containing x^-19 in the expansion (-3x+1/x^6)^9

Answer 1

Answer 2

(-3x + 1/x^6)^9

has 10 terms, only term including x^-19 is the 5th term

use the formula (a+b)^n + a^n +(n)a^(n-1)b + nC2)(a^(n-2)b^2 + (nC3)(a^(n-3)b^3 - (nC4)(a^(n-4)b^4 +

.... + b^n

where a=-3x, b= 1/x^6, n=9

-3^9)x^9 + (9C1)(3^8)x^8/x^6 -(9C2)(3^7)x^7/x^12 + (9C3)(3^6)x^6/x^18- (9C4)(3^5)x^5/x^24 + ...

5th term =-(9C4)(3^5)x^-19 = (- 9!/5!4!)(243)x^-19

=- 30,618x^-19

this all assumes you meant [-3x +(1/x^6)]^9 and Not [(-3x+1)/x^6]^9