Solve y+2/y=1/x

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

Solve for x

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

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

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of y,x.

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

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

$$xy+2x=y$$

Combine all terms containing x.

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

Divide both sides by y+2.

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

Dividing by y+2 undoes the multiplication by y+2.

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

Variable x cannot be equal to 0.

$$x=\frac{y}{y+2}\text{, }x\neq 0$$

Solve for y

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

$$x\neq 0\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of y,x.

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

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

$$xy+2x=y$$

Subtract y from both sides.

$$xy+2x-y=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$xy-y=-2x$$

Combine all terms containing y.

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

Divide both sides by x-1.

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

Dividing by x-1 undoes the multiplication by x-1.

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

Variable y cannot be equal to 0.

$$y=-\frac{2x}{x-1}\text{, }y\neq 0$$