9. Find the ratio of the term independent of \( x \) in the expansion of \( \left(x-\frac{2}{x}\right)^{10} \) to the coefficient of \( x^{10} \) in the expansion of \( \left(1-x^{2}\right)^{10} \).
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The general term in the expansion of \((a + b)^n\) is given by: \[ T_k = \binom{n}{k} a^{n-k} b^k \] For \(\left(x - \frac{2}{x}\right)^{10}\), let \(a = x\) and \(b = -\frac{2}{x}\). The general term is: \[ T_k = \binom{10}{k} x^{10-k} Show more…
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