Solve 2/x-3/y=1/z

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

Solve for x

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

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

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 xyz, the least common multiple of x,y,z.

$$yz\times 2-xz\times 3=xy$$

Subtract xy from both sides.

$$yz\times 2-xz\times 3-xy=0$$

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

$$-xz\times 3-xy=-yz\times 2$$

Multiply -1 and 3 to get -3.

$$-3xz-xy=-yz\times 2$$

Multiply -1 and 2 to get -2.

$$-3xz-xy=-2yz$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -3z-y.

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

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

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

Divide -2yz by -3z-y.

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

Variable x cannot be equal to 0.

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

Solve for y

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

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

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 xyz, the least common multiple of x,y,z.

$$yz\times 2-xz\times 3=xy$$

Subtract xy from both sides.

$$yz\times 2-xz\times 3-xy=0$$

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

$$yz\times 2-xy=xz\times 3$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 2z-x.

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

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

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

Variable y cannot be equal to 0.

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