Solve 1/x+1/y=1/12

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 12 }$$

Solve for x

$$x=-\frac{12y}{12-y}$$

$$y\neq 0\text{ and }y\neq 12$$

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 12xy, the least common multiple of x,y,12.

$$12y+12x=xy$$

Subtract xy from both sides.

$$12y+12x-xy=0$$

Subtract 12y from both sides. Anything subtracted from zero gives its negation.

$$12x-xy=-12y$$

Combine all terms containing x.

$$\left(12-y\right)x=-12y$$

Divide both sides by 12-y.

$$\frac{\left(12-y\right)x}{12-y}=-\frac{12y}{12-y}$$

Dividing by 12-y undoes the multiplication by 12-y.

$$x=-\frac{12y}{12-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{12y}{12-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{12x}{12-x}$$

$$x\neq 0\text{ and }x\neq 12$$

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 12xy, the least common multiple of x,y,12.

$$12y+12x=xy$$

Subtract xy from both sides.

$$12y+12x-xy=0$$

Subtract 12x from both sides. Anything subtracted from zero gives its negation.

$$12y-xy=-12x$$

Combine all terms containing y.

$$\left(12-x\right)y=-12x$$

Divide both sides by 12-x.

$$\frac{\left(12-x\right)y}{12-x}=-\frac{12x}{12-x}$$

Dividing by 12-x undoes the multiplication by 12-x.

$$y=-\frac{12x}{12-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{12x}{12-x}\text{, }y\neq 0$$