Solve 1/x+1/y=1/15

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 15 }$$

Solve for x

$$x=-\frac{15y}{15-y}$$

$$y\neq 0\text{ and }y\neq 15$$

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 15xy, the least common multiple of x,y,15.

$$15y+15x=xy$$

Subtract xy from both sides.

$$15y+15x-xy=0$$

Subtract 15y from both sides. Anything subtracted from zero gives its negation.

$$15x-xy=-15y$$

Combine all terms containing x.

$$\left(15-y\right)x=-15y$$

Divide both sides by 15-y.

$$\frac{\left(15-y\right)x}{15-y}=-\frac{15y}{15-y}$$

Dividing by 15-y undoes the multiplication by 15-y.

$$x=-\frac{15y}{15-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{15y}{15-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{15x}{15-x}$$

$$x\neq 0\text{ and }x\neq 15$$

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 15xy, the least common multiple of x,y,15.

$$15y+15x=xy$$

Subtract xy from both sides.

$$15y+15x-xy=0$$

Subtract 15x from both sides. Anything subtracted from zero gives its negation.

$$15y-xy=-15x$$

Combine all terms containing y.

$$\left(15-x\right)y=-15x$$

Divide both sides by 15-x.

$$\frac{\left(15-x\right)y}{15-x}=-\frac{15x}{15-x}$$

Dividing by 15-x undoes the multiplication by 15-x.

$$y=-\frac{15x}{15-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{15x}{15-x}\text{, }y\neq 0$$