I had to calculate $\frac{dy}{dx}$ for the equation $2x^2 = \frac{x+y}{x-y}$
If I rearrange the equation like this: $2x^2(x-y) = x+y$
Now when I calculate $\frac{dy}{dx}$ for the above 2 equations, I get different answers Why is this? I checked my answers on Wolfram Alpha too
The answer for equation 1: $\frac{2x^3-4x^2y+2xy^2+y}{x}$
The answer for equation 2: $\frac{6x^2-4xy-1}{2x^2+1}$
The answers are the same. If you replace $2x^2$ in the second solution in both places with $\frac{x+y}{x-y}$, you can turn one answer into the other.