If `y=(1+1/(x^2))/(1-1/(x^2))`, then `(dy)/(dx)`= a. `-(4x)/((x^2-1)^2)` b. `-(4x)/(x^2-1)` c. `(1-x^2)/(4x)` d. `(4x)/(x^2-1)`

Explanation

To find the derivative of the function \( y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}} \), we will follow these steps:

### Step 1: Simplify the Expression
First, we can simplify the expression for \( y \):
\[ y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}} = \frac{\frac{x^2 + 1}{x^2}}{\frac{x^2 - 1}{x^2}} = \frac{x^2 + 1}{x^2 - 1} \]

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