Ok, I have a question here, however the problem i have is more simple than the actual question itself, it's a basic math lack of understanding on my part.

Consider the curve defined by:

$\displaystyle x^2 + 4xy + y^2 = 6$

Find an expression for $\displaystyle \frac{dy}{dx}$ in terms of x and y, and hence give the equation of the tangent to the curve at the point (x,y) = (1,1)

So, to begin, I make:

$\displaystyle x^2 + 4xy + y^2 = 0$

then differentiate with respect to X:

giving $\displaystyle \frac{dy}{dx} = 2x+4y$

Next, differentiate with respect to Y:

giving $\displaystyle \frac{dx}{dy} = 4x + 2y$

Now, I know that the next step is $\displaystyle \frac{dy}{dx} = -\frac{2x+4y}{4x+2y}$

But I don't understand where the - comes from to make the fraction negative. I know that $\displaystyle \frac{dx}{dy}$ needs to be inverted to make it into $\displaystyle \frac{dy}{dx}$ and so moving to the bottom ofthe fraction, but where does the minus sign come from?

Could someone please explain that before we move onto the next step? Thanks