Solve 3/x-2/y=3

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

Solve for x

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

$$y\neq 0\text{ and }y\neq -\frac{2}{3}$$

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.

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

Subtract 3xy from both sides.

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

Subtract y\times 3 from both sides. Anything subtracted from zero gives its negation.

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

Multiply -1 and 2 to get -2.

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

Multiply -1 and 3 to get -3.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -2-3y.

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

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

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

Divide -3y by -2-3y.

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

Variable x cannot be equal to 0.

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

Solve for y

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

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

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.

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

Subtract 3xy from both sides.

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

Add x\times 2 to both sides. Anything plus zero gives itself.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by -3x+3.

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

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

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

Divide 2x by -3x+3.

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

Variable y cannot be equal to 0.

$$y=\frac{2x}{3\left(1-x\right)}\text{, }y\neq 0$$