Solve x^2-4/x^2+2x=y

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

Solve for y

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

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

Steps for Solving Linear Equation

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

$$x^{2}-4=yx\left(x+2\right)$$

Use the distributive property to multiply yx by x+2.

$$x^{2}-4=yx^{2}+2yx$$

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

$$yx^{2}+2yx=x^{2}-4$$

Combine all terms containing y.

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

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

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

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

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

Divide x^{2}-4 by x^{2}+2x.

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

Solve for x

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

$$y\neq 2\text{ and }y\neq 1$$