Solve 1/x=1/y

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

Solve for x

$$x=y$$

$$y\neq 0$$

Solution Steps

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 x,y.

$$y=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=y$$

Variable x cannot be equal to 0.

$$x=y\text{, }x\neq 0$$

Solve for y

$$y=x$$

$$x\neq 0$$

Solution Steps

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 x,y.

$$y=x$$

Variable y cannot be equal to 0.

$$y=x\text{, }y\neq 0$$