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

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

Solve for y (complex solution)

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

$$x\neq -i\text{ and }x\neq i$$

Steps for Solving Linear Equation

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

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

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

$$\left(2yx-2iy\right)\left(x+i\right)=x^{2}$$

Use the distributive property to multiply 2yx-2iy by x+i and combine like terms.

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

Combine all terms containing y.

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

Divide both sides by 2+2x^{2}.

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

Dividing by 2+2x^{2} undoes the multiplication by 2+2x^{2}.

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

Divide x^{2} by 2+2x^{2}.

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

Solve for y

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

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 2y by x^{2}+1.

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

Combine all terms containing y.

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

Divide both sides by 2x^{2}+2.

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

Dividing by 2x^{2}+2 undoes the multiplication by 2x^{2}+2.

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

Divide x^{2} by 2x^{2}+2.

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

Solve for x (complex solution)

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

$$x=i\left(2y-1\right)^{-\frac{1}{2}}\sqrt{2y}\text{, }y\neq \frac{1}{2}$$

Solve for x

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

$$x=-\sqrt{-\frac{2y}{2y-1}}\text{, }y\geq 0\text{ and }y<\frac{1}{2}$$