2×/x-1 + 3/x+1 rational algebraic expression

To simplify the rational algebraic expression \( \frac{2x}{x-1} + \frac{3}{x+1} \), we first need to find a common denominator and combine the terms.

1. **Identify the denominators**: \( x-1 \) and \( x+1 \).

2. **Find the least common denominator (LCD)**: The LCD of \( x-1 \) and \( x+1 \) is \( (x-1)(x+1) \).

3. **Rewrite each fraction with the LCD**:
   \[
   \frac{2x}{x-1} = \frac{2x(x+1)}{(x-1)(x+1)}
   \]
   \[
   \frac{3}{x+1} = \frac{3(x-1)}{(x+1)(x-1)}
   \]

4. **Combine the fractions**:
   \[
   \frac{2x(x+1)}{(x-1)(x+1)} + \frac{3(x-1)}{(x+1)(x-1)} = \frac{2x(x+1) + 3(x-1)}{(x-1)(x+1)}
   \

Learn how to simplify the rational algebraic expression 2x/(x-1) + 3/(x+1) step-by-step with detailed explanations. This problem involves rational expressions and simplification techniques. Suitable for high school students.

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