Solve x+y/2xy=50

$$\frac { x + y } { 2 x y } = 50$$

Solve for x

$$x=-\frac{y}{1-100y}$$

$$y\neq 0\text{ and }y\neq \frac{1}{100}$$

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 2xy.

$$x+y=100xy$$

Subtract 100xy from both sides.

$$x+y-100xy=0$$

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

$$x-100xy=-y$$

Combine all terms containing x.

$$\left(1-100y\right)x=-y$$

Divide both sides by 1-100y.

$$\frac{\left(1-100y\right)x}{1-100y}=-\frac{y}{1-100y}$$

Dividing by 1-100y undoes the multiplication by 1-100y.

$$x=-\frac{y}{1-100y}$$

Variable x cannot be equal to 0.

$$x=-\frac{y}{1-100y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{x}{1-100x}$$

$$x\neq 0\text{ and }x\neq \frac{1}{100}$$

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 2xy.

$$x+y=100xy$$

Subtract 100xy from both sides.

$$x+y-100xy=0$$

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

$$y-100xy=-x$$

Combine all terms containing y.

$$\left(1-100x\right)y=-x$$

Divide both sides by 1-100x.

$$\frac{\left(1-100x\right)y}{1-100x}=-\frac{x}{1-100x}$$

Dividing by 1-100x undoes the multiplication by 1-100x.

$$y=-\frac{x}{1-100x}$$

Variable y cannot be equal to 0.

$$y=-\frac{x}{1-100x}\text{, }y\neq 0$$