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Using binomial theorem, write down the e...

Using binomial theorem, write down the expansions of the following:`\ (x+1-1/x)^3`

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`=\ ^{3} C_{0}(x+1)^{3}(frac{1}{x})^{0}-\ ^{3} C_{1}(x+1)^{2}(frac{1}{x})^{1}+\ ^{3} C_{2}(x+1)^{1}(frac{1}{x})^{2}-\ ^{3} C_{3}(x+1)^{0}(frac{1}{x})^{3}`
`=(x+1)^{3}-3(x+1)^{2} times frac{1}{x}+3 frac{x+1}{x^{2}}-frac{1}{x^{3}}`
=`x^{3}+1+3 x+3 x^{2}-frac{3 x^{2}+3+6 x}{x+1}+3 frac{x}{x^{2}}-frac{1}{x^{3}}`
`=x^{3}+1+3 x+3 x^{2}-3 x-frac{3}{x}-6+frac{3}{x}+frac{3}{x^{2}}-frac{1}{x^{3}} `
`=x^{3}+3 x^{2}-5+frac{3}{x^{2}}-frac{1}{x^{3}}`
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