Solve 2x+2y/x^2-2x=1

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

Solve for y

$$y=-\frac{x\left(4-x\right)}{2}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x-2\right).

$$2x+2y=x\left(x-2\right)$$

Use the distributive property to multiply x by x-2.

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

Subtract 2x from both sides.

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

Combine -2x and -2x to get -4x.

$$2y=x^{2}-4x$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{x\left(x-4\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{x\left(x-4\right)}{2}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\sqrt{2y+4}+2\text{, }&y\neq -2\\x=-\sqrt{2y+4}+2\text{, }&y\neq -2\text{ and }y\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{2y+4}+2\text{, }&y>-2\\x=-\sqrt{2y+4}+2\text{, }&y\neq 0\text{ and }y>-2\end{matrix}\right.$$