Differentiate `((x^(2) + 5x -6)/(4x^(2) -x+3))`

Explanation

To differentiate the function \( y = \frac{x^2 + 5x - 6}{4x^2 - x + 3} \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), where both \( u \) and \( v \) are functions of \( x \), then the derivative \( \frac{dy}{dx} \) is given by:

\[ \frac{dy}{dx} = \frac{u'v - uv'}{v^2} \]

where \( u' \) is the derivative of \( u \) and \( v' \) is the derivative of \( v \).

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