I'm studying for my calc final tomorrow, and am going through some practice questions and I'm not sure if the solution is wrong or I'm just miss understanding.
The question is about finding a tangent line to a curve and point P. The equation of the curve is $x^3+x^2y+y^2=7$ and after differentiating I got the answer $\frac{-3x^2-2xy}{x^2+2y}$ however in the solutions it says $\frac{-3x^2-2xy}{x^2+2xy}$
I'm confused how in the denominator $x^2+2xy$, here's my work that I did:
$$x^3+x^2y+y^2=7$$
$$3x^2+2xy+x^2\frac{dy}{dx}+2y\frac{dy}{dx}=0$$
$$x^2\frac{dy}{dx}+2y\frac{dy}{dx}=-3x^2-2xy$$
$$\frac{dy}{dx} = \frac{-3x^2-2xy}{x^2+2y}$$
As the comments pointed out, your answer is correct, and the error in your book is probably due to a typo. Anyway you can verify your answer here.