Solve 1/x+1/y=1/2013

$$\frac{ 1 }{ x } + \frac{ 1 }{ y } = \frac{ 1 }{ 2013 }$$

Solve for x

$$x=-\frac{2013y}{2013-y}$$

$$y\neq 0\text{ and }y\neq 2013$$

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 2013xy, the least common multiple of x,y,2013.

$$2013y+2013x=xy$$

Subtract xy from both sides.

$$2013y+2013x-xy=0$$

Subtract 2013y from both sides. Anything subtracted from zero gives its negation.

$$2013x-xy=-2013y$$

Combine all terms containing x.

$$\left(2013-y\right)x=-2013y$$

Divide both sides by 2013-y.

$$\frac{\left(2013-y\right)x}{2013-y}=-\frac{2013y}{2013-y}$$

Dividing by 2013-y undoes the multiplication by 2013-y.

$$x=-\frac{2013y}{2013-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{2013y}{2013-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{2013x}{2013-x}$$

$$x\neq 0\text{ and }x\neq 2013$$

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 2013xy, the least common multiple of x,y,2013.

$$2013y+2013x=xy$$

Subtract xy from both sides.

$$2013y+2013x-xy=0$$

Subtract 2013x from both sides. Anything subtracted from zero gives its negation.

$$2013y-xy=-2013x$$

Combine all terms containing y.

$$\left(2013-x\right)y=-2013x$$

Divide both sides by 2013-x.

$$\frac{\left(2013-x\right)y}{2013-x}=-\frac{2013x}{2013-x}$$

Dividing by 2013-x undoes the multiplication by 2013-x.

$$y=-\frac{2013x}{2013-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{2013x}{2013-x}\text{, }y\neq 0$$