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

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

Solve for y (complex solution)

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

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$2xy=4x^{2}+1-1$$

Subtract 1 from 1 to get 0.

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

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

Subtract 1 from both sides.

$$2xy=4x^{2}+1-1$$

Subtract 1 from 1 to get 0.

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

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

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

$$x=0$$