To solve the inequality:

\[
\frac{2}{x+1} > x - \frac{1}{x+1}
\]

we first need to combine like terms by getting everything over a common denominator.

### Step 1: Combine like terms

The common denominator is \(x + 1\), so we can rewrite the inequality as:

\[
\frac{2}{x+1} > \frac{x(x+1)}{x+1} - \frac{1}{x+1}
\]

Simplify the right-hand side:

\[
\frac{2}{x+1} > \frac{x^2 + x - 1}{x+1}
\]

Now, we have:

\[
\frac{2}{x+1} > \frac{x^2 + x - 1}{x+1}
\]

### Step 2: Cross-multiply and solve

Since the denominators are the same, we can compare the numerators directly:

\[
2 > x^2 + x - 1
\]

Rearrange to form a quadratic inequality:

\[
x^2 + x - 3 < 0
\]

### Step 

Learn how to solve the rational inequality 2/(x+1) > x - 1/(x+1) step-by-step with detailed explanations. This problem involves inequalities and rational expressions, suitable for advanced high school students.

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