How to solve 1/x=1/y-1/z

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 1/x=1/y-1/z | Equatix

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Question

$$1/x=1/y-1/z$$

Solve for x

$x=-\frac{yz}{y-z}$
$z\neq 0\text{ and }y\neq 0\text{ and }y\neq z$

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 $x,y,z$.

$$yz=xz-xy$$

Swap sides so that all variable terms are on the left hand side.

$$xz-xy=yz$$

Reorder the terms.

$$-xy+xz=yz$$

Combine all terms containing $x$.

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

The equation is in standard form.

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

Divide both sides by $z-y$.

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

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

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

Variable $x$ cannot be equal to $0$.

$$x=\frac{yz}{z-y}\text{, }x\neq 0$$

Show Solution

Solve for y

$y=\frac{xz}{x+z}$
$z\neq 0\text{ and }x\neq 0\text{ and }x\neq -z$

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 $x,y,z$.

$$yz=xz-xy$$

Add $xy$ to both sides.

$$yz+xy=xz$$

Combine all terms containing $y$.

$$\left(z+x\right)y=xz$$

The equation is in standard form.

$$\left(x+z\right)y=xz$$

Divide both sides by $x+z$.

$$\frac{\left(x+z\right)y}{x+z}=\frac{xz}{x+z}$$

Dividing by $x+z$ undoes the multiplication by $x+z$.

$$y=\frac{xz}{x+z}$$

Variable $y$ cannot be equal to $0$.

$$y=\frac{xz}{x+z}\text{, }y\neq 0$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for x

Steps for Solving Linear Equation

Solve for y

Steps for Solving Linear Equation