Solve 2/x-1/y=3

$$\frac{ 2 }{ x } - \frac{ 1 }{ y } = 3$$

Solve for x

$$x=\frac{2y}{3y+1}$$

$$y\neq 0\text{ and }y\neq -\frac{1}{3}$$

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.

$$y\times 2-x=3xy$$

Subtract 3xy from both sides.

$$y\times 2-x-3xy=0$$

Subtract y\times 2 from both sides. Anything subtracted from zero gives its negation.

$$-x-3xy=-y\times 2$$

Multiply -1 and 2 to get -2.

$$-x-3xy=-2y$$

Combine all terms containing x.

$$\left(-1-3y\right)x=-2y$$

The equation is in standard form.

$$\left(-3y-1\right)x=-2y$$

Divide both sides by -1-3y.

$$\frac{\left(-3y-1\right)x}{-3y-1}=-\frac{2y}{-3y-1}$$

Dividing by -1-3y undoes the multiplication by -1-3y.

$$x=-\frac{2y}{-3y-1}$$

Divide -2y by -1-3y.

$$x=\frac{2y}{3y+1}$$

Variable x cannot be equal to 0.

$$x=\frac{2y}{3y+1}\text{, }x\neq 0$$

Solve for y

$$y=\frac{x}{2-3x}$$

$$x\neq 0\text{ and }x\neq \frac{2}{3}$$

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.

$$y\times 2-x=3xy$$

Subtract 3xy from both sides.

$$y\times 2-x-3xy=0$$

Add x to both sides. Anything plus zero gives itself.

$$y\times 2-3xy=x$$

Combine all terms containing y.

$$\left(2-3x\right)y=x$$

Divide both sides by 2-3x.

$$\frac{\left(2-3x\right)y}{2-3x}=\frac{x}{2-3x}$$

Dividing by 2-3x undoes the multiplication by 2-3x.

$$y=\frac{x}{2-3x}$$

Variable y cannot be equal to 0.

$$y=\frac{x}{2-3x}\text{, }y\neq 0$$