Multiple Choice 1 point For the curve x^2+xy+y^2=5 which of the following is equal to (dy)/(dx) (2x-y)/(x+2y) (2x+y)/(x+2y) (y-2x)/(x+2y) -(2x+y)/(x+2y)

To find $\frac{dy}{dx}$ for the given curve $x^2 + xy + y^2 = 5$, we need to differentiate both sides of the equation with respect to $x$.<br /><br />Differentiating the left side with respect to $x$, we get:<br />$2x + y + x\frac{dy}{dx} + 2y\frac{dy}{dx} = 0$<br /><br />Simplifying, we have:<br />$2x + y + (x + 2y)\frac{dy}{dx} = 0$<br /><br />Now, we can solve for $\frac{dy}{dx}$:<br />$\frac{dy}{dx} = \frac{2x - y}{x + 2y}$<br /><br />Therefore, the correct answer is $\frac{2x - y}{x + 2y}$.