Differentiate with respect to x to the given function`(3x+4)/(5x^(2)-7x+9)`

Explanation

To differentiate the function \( y = \frac{3x + 4}{5x^2 - 7x + 9} \) with respect to \( x \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( \frac{f(x)}{g(x)} \), then the derivative is given by:

\[ \frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2} \]

### Step-by-Step Solution:

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