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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 $$\frac {dz}{dx}$$

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Let $u=4x+7y$, now we get: $du/dx=4+7dy/dx$

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    When you have $$\frac{dy}{dx}=f\bigg(\frac{ax+by+c}{a'x+b'y+c'}\bigg)$$ and $\frac{a}{a'}=\frac{b}{b'}$, so you can take $ax+by+c=t$ as a substitution. After that find $a'x+b'y+c'$ according to $t$ and solve the resulted ODE.2012-11-15
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    It is customary to take whole $4x+7y+2$ as $u$.2012-11-15
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    Thanks @BabakSorouh for detailed explanation :)2012-11-15
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    Furthermore i stuck here $$ \frac 17 (\frac {dz}{dx}-4) = \frac {z+2}{z+3}$$ I need the value of $$\frac {dz}{dx}$$2012-11-15
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    @TPSstar: See my second comment above and do the same with that substitution again.2012-11-15