Solve f:y=x^2+2/x-2

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

Solve for f

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by y\left(x-2\right), the least common multiple of y,x-2.

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

Use the distributive property to multiply x-2 by f.

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

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

$$xf-2f=yx^{2}+2y$$

Combine all terms containing f.

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

Divide both sides by x-2.

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

Dividing by x-2 undoes the multiplication by x-2.

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{f^{2}-8fy-8y^{2}}-f}{2y}$$

$$x=\frac{\sqrt{f^{2}-8fy-8y^{2}}+f}{2y}\text{, }y\neq 0$$

Solve for x

$$x=-\frac{\sqrt{f^{2}-8fy-8y^{2}}-f}{2y}$$

$$x=\frac{\sqrt{f^{2}-8fy-8y^{2}}+f}{2y}\text{, }y\neq 0\text{ and }\left(f\geq 2\sqrt{6}|y|+4y\text{ or }f\leq -2\sqrt{6}|y|+4y\right)$$