How to solve 68/21=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 68/21=x+1/y+1/z | Equatix

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Question

$$68/21=x+1/y+1/z$$

Solve for x

$x=\frac{68yz-21y-21z}{21yz}$
$z\neq 0\text{ and }y\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $21yz$, the least common multiple of $21,y,z$.

$$68yz=21yzx+21z+21y$$

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

$$21yzx+21z+21y=68yz$$

Subtract $21z$ from both sides.

$$21yzx+21y=68yz-21z$$

Subtract $21y$ from both sides.

$$21yzx=68yz-21z-21y$$

The equation is in standard form.

$$21yzx=68yz-21y-21z$$

Divide both sides by $21yz$.

$$\frac{21yzx}{21yz}=\frac{68yz-21y-21z}{21yz}$$

Dividing by $21yz$ undoes the multiplication by $21yz$.

$$x=\frac{68yz-21y-21z}{21yz}$$

Divide $68yz-21z-21y$ by $21yz$.

$$x=\frac{68}{21}-\frac{1}{y}-\frac{1}{z}$$

Show Solution

Solve for y

$y=-\frac{21z}{21xz-68z+21}$
$z\neq 0\text{ and }x\neq \frac{68}{21}-\frac{1}{z}$

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 $21yz$, the least common multiple of $21,y,z$.

$$68yz=21yzx+21z+21y$$

Subtract $21yzx$ from both sides.

$$68yz-21yzx=21z+21y$$

Subtract $21y$ from both sides.

$$68yz-21yzx-21y=21z$$

Combine all terms containing $y$.

$$\left(68z-21zx-21\right)y=21z$$

The equation is in standard form.

$$\left(-21xz+68z-21\right)y=21z$$

Divide both sides by $68z-21zx-21$.

$$\frac{\left(-21xz+68z-21\right)y}{-21xz+68z-21}=\frac{21z}{-21xz+68z-21}$$

Dividing by $68z-21zx-21$ undoes the multiplication by $68z-21zx-21$.

$$y=\frac{21z}{-21xz+68z-21}$$

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

$$y=\frac{21z}{-21xz+68z-21}\text{, }y\neq 0$$

Show Solution

Basic Math

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Example

Question

Solve for x

Steps for Solving Linear Equation

Solve for y

Steps for Solving Linear Equation