Solve frac{sqrt{x^2-4}+sqrt{4-x^2}+1}{x-2}=y

$$\frac { \sqrt { x ^ { 2 } - 4 } + \sqrt { 4 - x ^ { 2 } } + 1 } { x - 2 } = y$$

Solve for y (complex solution)

$$y=-\frac{\sqrt{4-x^{2}}+\sqrt{-\left(4-x^{2}\right)}+1}{2-x}$$

$$x\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$\sqrt{x^{2}-4}+\sqrt{4-x^{2}}+1=y\left(x-2\right)$$

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

$$\sqrt{x^{2}-4}+\sqrt{4-x^{2}}+1=yx-2y$$

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

$$yx-2y=\sqrt{x^{2}-4}+\sqrt{4-x^{2}}+1$$

Combine all terms containing y.

$$\left(x-2\right)y=\sqrt{x^{2}-4}+\sqrt{4-x^{2}}+1$$

The equation is in standard form.

$$\left(x-2\right)y=\sqrt{4-x^{2}}+\sqrt{-\left(4-x^{2}\right)}+1$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)y}{x-2}=\frac{\sqrt{4-x^{2}}+\sqrt{-\left(4-x^{2}\right)}+1}{x-2}$$

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

$$y=\frac{\sqrt{4-x^{2}}+\sqrt{-\left(4-x^{2}\right)}+1}{x-2}$$

Solve for y

$$y=-\frac{1}{4}=-0.25$$

$$x=-2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$\sqrt{x^{2}-4}+\sqrt{4-x^{2}}+1=y\left(x-2\right)$$

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

$$\sqrt{x^{2}-4}+\sqrt{4-x^{2}}+1=yx-2y$$

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

$$yx-2y=\sqrt{x^{2}-4}+\sqrt{4-x^{2}}+1$$

Combine all terms containing y.

$$\left(x-2\right)y=\sqrt{x^{2}-4}+\sqrt{4-x^{2}}+1$$

The equation is in standard form.

$$\left(x-2\right)y=\sqrt{4-x^{2}}+\sqrt{-\left(4-x^{2}\right)}+1$$

Divide both sides by -2+x.

$$\frac{\left(x-2\right)y}{x-2}=\frac{\sqrt{4-x^{2}}+\sqrt{-\left(4-x^{2}\right)}+1}{x-2}$$

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

$$y=\frac{\sqrt{4-x^{2}}+\sqrt{-\left(4-x^{2}\right)}+1}{x-2}$$

Divide \sqrt{-\left(-x^{2}+4\right)}+\sqrt{4-x^{2}}+1 by -2+x.

$$y=-\frac{\sqrt{4-x^{2}}+\sqrt{-\left(4-x^{2}\right)}+1}{2-x}$$