Given that `y=(x^(2)+1)/(x-2)`, find `(dy)/(dx)`

Explanation

To find the derivative of the function \( y = \frac{x^2 + 1}{x - 2} \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form of \( \frac{u}{v} \), then the derivative is given by:

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

where \( u = x^2 + 1 \) and \( v = x - 2 \).

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