((x-1)/(x+1))^n give me the first 3 terms

To find the first three terms of the expansion of \(\left(\frac{x-1}{x+1}\right)^n\), we can apply the binomial series expansion for \(\left(1 + u\right)^n\), where \(u = \frac{-2}{x+1}\).

Let's go through the steps:

1. **Rewrite the expression:**

   \[
   \left(\frac{x-1}{x+1}\right)^n = \left(1 + \frac{-2}{x+1}\right)^n
   \]

2. **Apply the binomial expansion:**

   The binomial expansion for \((1 + u)^n\) is:

   \[
   (1 + u)^n = 1 + nu + \frac{n(n-1)}{2}u^2 + \cdots
   \]

3. **Substitute \( u = \frac{-2}{x+1} \):**

   Using this in the binomial expansion gives the first three terms:

   \[
   \left(\frac{x-1}{x+1}\right)^n = 1 + n\left(\frac{-2}{x+1}\right) + \frac{n(n-1)}{2}\left(\frac{-2}{x+1}\right)^2 + \cdots
   \]

4. **Simplify the first three terms:**

   \[
   \left(\frac{x-1}{x+1}\right)^n = 1 - \frac{2n}{x+1} + \frac

Find the first three terms of the expansion of ((x-1)/(x+1))^n using the binomial theorem. This step-by-step solution covers algebraic concepts including series expansion and simplification, suitable for advanced high school students in Grades 11-12.

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