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

Explanation

To differentiate the function \( y = \frac{x^2 - x + 1}{x^2 + x + 1} \) with respect to \( x \), we will use the quotient rule for differentiation. The quotient rule states that if you have a function \( y = \frac{u}{v} \), then the derivative \( \frac{dy}{dx} \) is given by:

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

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

...