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

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

Solve for y

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

Steps for Solving Linear Equation

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

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

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

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

Swap sides so that all variable terms are on the left hand side.

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

Combine all terms containing y.

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

Divide both sides by x^{2}+1.

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

Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.

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

Solve for x

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

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