Solve y=1+2/1-2{1+frac{2/x}}

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

Solve for x (complex solution)

$$x=-\frac{2\left(3-y\right)}{y+1}$$

$$y\neq -1\text{ and }y\neq 1\text{ and }y\neq 3$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

Since \frac{x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

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

Variable x cannot be equal to 0 since division by zero is not defined. Divide 2 by \frac{x+2}{x} by multiplying 2 by the reciprocal of \frac{x+2}{x}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.

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

Since \frac{x+2}{x+2} and \frac{2x}{x+2} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in x+2-2x.

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

Variable x cannot be equal to -2 since division by zero is not defined. Divide 2 by \frac{-x+2}{x+2} by multiplying 2 by the reciprocal of \frac{-x+2}{x+2}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{-x+2}{-x+2}.

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

Since \frac{-x+2}{-x+2} and \frac{2\left(x+2\right)}{-x+2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -x+2+2\left(x+2\right).

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

Combine like terms in -x+2+2x+4.

$$y=\frac{x+6}{-x+2}$$

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

$$\frac{x+6}{-x+2}=y$$

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -x+2.

$$x+6=y\left(-x+2\right)$$

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

$$x+6=-yx+2y$$

Add yx to both sides.

$$x+6+yx=2y$$

Subtract 6 from both sides.

$$x+yx=2y-6$$

Combine all terms containing x.

$$\left(1+y\right)x=2y-6$$

The equation is in standard form.

$$\left(y+1\right)x=2y-6$$

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=\frac{2y-6}{y+1}$$

Dividing by y+1 undoes the multiplication by y+1.

$$x=\frac{2y-6}{y+1}$$

Divide -6+2y by y+1.

$$x=\frac{2\left(y-3\right)}{y+1}$$

Variable x cannot be equal to any of the values 2,-2,0.

$$x=\frac{2\left(y-3\right)}{y+1}\text{, }x\neq 2\text{ and }x\neq -2\text{ and }x\neq 0$$

Solve for x

$$x=-\frac{2\left(3-y\right)}{y+1}$$

$$y\neq 3\text{ and }|y|\neq 1$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

Since \frac{x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

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

Variable x cannot be equal to 0 since division by zero is not defined. Divide 2 by \frac{x+2}{x} by multiplying 2 by the reciprocal of \frac{x+2}{x}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.

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

Since \frac{x+2}{x+2} and \frac{2x}{x+2} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in x+2-2x.

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

Variable x cannot be equal to -2 since division by zero is not defined. Divide 2 by \frac{-x+2}{x+2} by multiplying 2 by the reciprocal of \frac{-x+2}{x+2}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{-x+2}{-x+2}.

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

Since \frac{-x+2}{-x+2} and \frac{2\left(x+2\right)}{-x+2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -x+2+2\left(x+2\right).

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

Combine like terms in -x+2+2x+4.

$$y=\frac{x+6}{-x+2}$$

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

$$\frac{x+6}{-x+2}=y$$

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -x+2.

$$x+6=y\left(-x+2\right)$$

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

$$x+6=-yx+2y$$

Add yx to both sides.

$$x+6+yx=2y$$

Subtract 6 from both sides.

$$x+yx=2y-6$$

Combine all terms containing x.

$$\left(1+y\right)x=2y-6$$

The equation is in standard form.

$$\left(y+1\right)x=2y-6$$

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=\frac{2y-6}{y+1}$$

Dividing by y+1 undoes the multiplication by y+1.

$$x=\frac{2y-6}{y+1}$$

Divide -6+2y by y+1.

$$x=\frac{2\left(y-3\right)}{y+1}$$

Variable x cannot be equal to any of the values 2,-2,0.

$$x=\frac{2\left(y-3\right)}{y+1}\text{, }x\neq 2\text{ and }x\neq -2\text{ and }x\neq 0$$

Solve for y (complex solution)

$$y=\frac{x+6}{2-x}$$

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

Solve for y

$$y=\frac{x+6}{2-x}$$

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