Differentiate `(sqrt(x^2+1)+sqrt(x^2-1))/(sqrt(x^2+1)-sqrt(x^2-1))` with respect to `x` .

Explanation

To differentiate the function \( y = \frac{\sqrt{x^2 + 1} + \sqrt{x^2 - 1}}{\sqrt{x^2 + 1} - \sqrt{x^2 - 1}} \) with respect to \( x \), we will use the quotient rule and the chain rule.

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = \frac{\sqrt{x^2 + 1} + \sqrt{x^2 - 1}}{\sqrt{x^2 + 1} - \sqrt{x^2 - 1}} \]
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