Solve 2/x+3/y=3

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

Solve for x

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

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

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.

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

Subtract 3xy from both sides.

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

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

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

Multiply -1 and 2 to get -2.

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

Combine all terms containing x.

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

Divide both sides by -3y+3.

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

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

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

Divide -2y by -3y+3.

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

Variable x cannot be equal to 0.

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

Solve for y

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

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

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.

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

Subtract 3xy from both sides.

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

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

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

Multiply -1 and 3 to get -3.

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

Combine all terms containing y.

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

Divide both sides by 2-3x.

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

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

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

Variable y cannot be equal to 0.

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