Solve 2xy/1+x^2=4x^2/1+x^2

$$\frac { 2 x y } { 1 + x ^ { 2 } } = \frac { 4 x ^ { 2 } } { 1 + x ^ { 2 } }$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=2x\text{, }&x\neq -i\text{ and }x\neq i\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2xy=4x^{2}$$

Divide both sides by 2x.

$$\frac{2xy}{2x}=\frac{4x^{2}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$y=\frac{4x^{2}}{2x}$$

Divide 4x^{2} by 2x.

$$y=2x$$

Solve for y

$$\left\{\begin{matrix}\\y=2x\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}+1.

$$2xy=4x^{2}$$

Divide both sides by 2x.

$$\frac{2xy}{2x}=\frac{4x^{2}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$y=\frac{4x^{2}}{2x}$$

Divide 4x^{2} by 2x.

$$y=2x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{y}{2}\text{, }&y\neq -2i\text{ and }y\neq 2i\end{matrix}\right.$$

Solve for x

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

$$x=0$$