Differentiate each function by applying the basic rules of differentiation
`(2x^(2)+x+1)/(x^2-3x+2)`

Explanation

To differentiate the function \( y = \frac{2x^2 + x + 1}{x^2 - 3x + 2} \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( y = \frac{u}{v} \), where \( u \) and \( v \) are both functions of \( x \), then the derivative \( \frac{dy}{dx} \) is given by:

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

Here, \( u = 2x^2 + x + 1 \) and \( v = x^2 - 3x + 2 \).

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