Solve 1/x-1/y=1/2

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

Solve for x

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

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

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 2xy, the least common multiple of x,y,2.

$$2y-2x=xy$$

Subtract xy from both sides.

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

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

$$-2x-xy=-2y$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -2-y.

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

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

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

Divide -2y by -2-y.

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

Variable x cannot be equal to 0.

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

Solve for y

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

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

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 2xy, the least common multiple of x,y,2.

$$2y-2x=xy$$

Subtract xy from both sides.

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

Add 2x to both sides. Anything plus zero gives itself.

$$2y-xy=2x$$

Combine all terms containing y.

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

Divide both sides by 2-x.

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

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

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

Variable y cannot be equal to 0.

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