Solve 2/x-3/y=1

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

Solve for x

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

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

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.

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

Subtract xy from both sides.

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

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

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

Multiply -1 and 3 to get -3.

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

Multiply -1 and 2 to get -2.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -3-y.

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

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

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

Divide -2y by -3-y.

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

Variable x cannot be equal to 0.

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

Solve for y

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

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

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.

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

Subtract xy from both sides.

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

Add x\times 3 to both sides. Anything plus zero gives itself.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 2-x.

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

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

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

Variable y cannot be equal to 0.

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