Solve x-2y=1-y/x

$$x-2y= \frac{ 1-y }{ x }$$

Solve for y

$$y=-\frac{x^{2}-1}{1-2x}$$

$$x\neq \frac{1}{2}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$xx-2yx=1-y$$

Multiply x and x to get x^{2}.

$$x^{2}-2yx=1-y$$

Add y to both sides.

$$x^{2}-2yx+y=1$$

Subtract x^{2} from both sides.

$$-2yx+y=1-x^{2}$$

Combine all terms containing y.

$$\left(-2x+1\right)y=1-x^{2}$$

The equation is in standard form.

$$\left(1-2x\right)y=1-x^{2}$$

Divide both sides by -2x+1.

$$\frac{\left(1-2x\right)y}{1-2x}=\frac{1-x^{2}}{1-2x}$$

Dividing by -2x+1 undoes the multiplication by -2x+1.

$$y=\frac{1-x^{2}}{1-2x}$$

Solve for x

$$\left\{\begin{matrix}\\x=\sqrt{y^{2}-y+1}+y\text{, }&\text{unconditionally}\\x=-\sqrt{y^{2}-y+1}+y\text{, }&y\neq 1\end{matrix}\right.$$