<s>[INST] Getting x in terms of y I have this equation:
$$\dfrac{x}{y} = \dfrac{y-x}{x}$$
How would I separate $x$ and $y$ in $x^2+xy-y^2=0$ ?
 [/INST] $$\frac{x}{y}=\frac{y-x}{x}$$
$$x^2=y(y-x)$$
$$x^2=y^2-yx$$
$$x^2+yx=y^2$$
$$x^2+yx+\left(\frac{y}{2}\right)^2=y^2+\left(\frac{y}{2}\right)^2$$
$$\left(x+\frac{y}{2}\right)^2=\frac{5}{4}y^2$$
$$x+\frac{y}{2}=\pm\sqrt{5}\frac{y}{2}$$
$$x=\frac{y}{2}(-1\pm\sqrt{5})$$
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