I'm supposed to implicitly differentiate $\sin(x+y)=2x-2y$. I've already taken the first derivative and got
$$ \left(\frac{dy}{dx}+1\right)\cdot\cos(y+x)=-2\left(\frac{dy}{dx}-1\right) $$
www.derivative-calculator.net says solving this equation for $\frac{dy}{dx}$ equals
$$ \frac{dy}{dx}=-\frac{\cos(y+x)-2}{\cos(y+x)+2} $$
But I'm lost when it comes to the algebra used to rewrite the equation in terms of $\frac{dy}{dx}$. Any help getting from point A to B will be greatly appreciated.