Find the coefficient of `x^9` in the expansion of `(x^2-1/(3x))^9`.

Explanation

Suppose `x^{9}` occurs at the `(r+1)` th term in the above expression.

Then, we have:

`T_{r+1}=\ ^{9} C_{r}(x^{2})^{9-r}(frac{-1}{3 x})^{r} `

`=(-1)^{r} 9 C_{r}(x^{18-2 r-r})(frac{1}{3^{r}})`

For this term to contain `x^{9}`, we must have:

`18-3 r=9 `

`Rightarrow 3 r=9 `

`Rightarrow r=3 `

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