Show that the expansion of `(x^2+1/x)^12` does not contain any term involving `x^(-1)dot`

Explanation

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

Then

`T_{r+1}=\ ^{12} C_{r}(x^{2})^{12-r}(frac{1}{x})^{r}`

`=\ ^{12} C_{r} x^{24-2 r-r}`

For this term to contain `x^{-1}`, we must have

`24-3 r=-1 `

`Rightarrow 3 r=25 `

`Rightarrow r=frac{25}{3}`

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