Differentiate each function by applying the basic rules of differentiation
`((t^(2)+1)/(t^(2)-1))`

Explanation

To differentiate the function \( y = \frac{t^2 + 1}{t^2 - 1} \), we will apply the quotient rule of differentiation. The quotient rule states that if you have a function in the form of \( \frac{u}{v} \), where both \( u \) and \( v \) are functions of \( t \), then the derivative \( \frac{dy}{dt} \) is given by:

\[ \frac{dy}{dt} = \frac{v \frac{du}{dt} - u \frac{dv}{dt}}{v^2} \]

### Step 1: Identify \( u \) and \( v \)
Let:
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