Please suggest appropriate substitution to reduce it to separable form
$$\frac{dy}{dx} = \frac{4x+7y+2}{4x+7y+3} $$
let $$z=4x+7y$$ then $$\frac{dz}{dx}=4+7\frac{dy}{dx}$$ $$ \frac {dy}{dx}= \frac17 (\frac{dz}{dx}-4) $$ $$\frac 17 (\frac {dz}{dx}-4) = \frac {z+2}{z+3}$$ please help further now i need the value of $$\frac {dz}{dx}$$