Solve 1/x+1/y=2007

$$\frac { 1 } { x } + \frac { 1 } { y } = 2007$$

Solve for x

$$x=-\frac{y}{1-2007y}$$

$$y\neq 0\text{ and }y\neq \frac{1}{2007}$$

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.

$$y+x=2007xy$$

Subtract 2007xy from both sides.

$$y+x-2007xy=0$$

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

$$x-2007xy=-y$$

Combine all terms containing x.

$$\left(1-2007y\right)x=-y$$

Divide both sides by 1-2007y.

$$\frac{\left(1-2007y\right)x}{1-2007y}=-\frac{y}{1-2007y}$$

Dividing by 1-2007y undoes the multiplication by 1-2007y.

$$x=-\frac{y}{1-2007y}$$

Variable x cannot be equal to 0.

$$x=-\frac{y}{1-2007y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{x}{1-2007x}$$

$$x\neq 0\text{ and }x\neq \frac{1}{2007}$$

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.

$$y+x=2007xy$$

Subtract 2007xy from both sides.

$$y+x-2007xy=0$$

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

$$y-2007xy=-x$$

Combine all terms containing y.

$$\left(1-2007x\right)y=-x$$

Divide both sides by 1-2007x.

$$\frac{\left(1-2007x\right)y}{1-2007x}=-\frac{x}{1-2007x}$$

Dividing by 1-2007x undoes the multiplication by 1-2007x.

$$y=-\frac{x}{1-2007x}$$

Variable y cannot be equal to 0.

$$y=-\frac{x}{1-2007x}\text{, }y\neq 0$$