Solve 1/x+1/y=2

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

Solve for x

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

$$y\neq 0\text{ and }y\neq \frac{1}{2}$$

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 xy, the least common multiple of x,y.

$$y+x=2xy$$

Subtract 2xy from both sides.

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

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

$$x-2xy=-y$$

Combine all terms containing x.

$$\left(1-2y\right)x=-y$$

Divide both sides by 1-2y.

$$\frac{\left(1-2y\right)x}{1-2y}=-\frac{y}{1-2y}$$

Dividing by 1-2y undoes the multiplication by 1-2y.

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

Variable x cannot be equal to 0.

$$x=-\frac{y}{1-2y}\text{, }x\neq 0$$

Solve for y

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

$$x\neq 0\text{ and }x\neq \frac{1}{2}$$

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 xy, the least common multiple of x,y.

$$y+x=2xy$$

Subtract 2xy from both sides.

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

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

$$y-2xy=-x$$

Combine all terms containing y.

$$\left(1-2x\right)y=-x$$

Divide both sides by 1-2x.

$$\frac{\left(1-2x\right)y}{1-2x}=-\frac{x}{1-2x}$$

Dividing by 1-2x undoes the multiplication by 1-2x.

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

Variable y cannot be equal to 0.

$$y=-\frac{x}{1-2x}\text{, }y\neq 0$$