Solve 1-2x/x+1-2y/y+1-2z/z=1/x+1/y+1/z= | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$1-2x/x+1-2y/y+1-2z/z=1/x+1/y+1/z=$$

Solve for x

$x=-\frac{yz}{3yz+y+z}$
$y\neq 0\text{ and }z\neq 0\text{ and }\left(z=-\frac{1}{3}\text{ or }y\neq -\frac{z}{3z+1}\right)$

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 $x,y,z$.

$$xyz-yz\times 2x+xyz-xz\times 2y+xyz-xy\times 2z=yz+xz+xy$$

Combine $xyz$ and $xyz$ to get $2xyz$.

$$2xyz-yz\times 2x-xz\times 2y+xyz-xy\times 2z=yz+xz+xy$$

Combine $-yz\times 2x$ and $-xz\times 2y$ to get $2\left(-yz\times 2x\right)$.

$$2xyz+2\left(-yz\times 2x\right)+xyz-xy\times 2z=yz+xz+xy$$

Combine $2xyz$ and $xyz$ to get $3xyz$.

$$3xyz+2\left(-yz\times 2x\right)-xy\times 2z=yz+xz+xy$$

Combine $2\left(-yz\times 2x\right)$ and $-xy\times 2z$ to get $3\left(-yz\times 2x\right)$.

$$3xyz+3\left(-yz\times 2x\right)=yz+xz+xy$$

Subtract $xz$ from both sides.

$$3xyz+3\left(-yz\times 2x\right)-xz=yz+xy$$

Subtract $xy$ from both sides.

$$3xyz+3\left(-yz\times 2x\right)-xz-xy=yz$$

Multiply $3$ and $-1$ to get $-3$.

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

Multiply $-3$ and $2$ to get $-6$.

$$3xyz-6yzx-xz-xy=yz$$

Combine $3xyz$ and $-6yzx$ to get $-3xyz$.

$$-3xyz-xz-xy=yz$$

Combine all terms containing $x$.

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

The equation is in standard form.

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

Divide both sides by $-y-z-3yz$.

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

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

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

Divide $yz$ by $-y-z-3yz$.

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

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

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

Solve for y

$y=-\frac{xz}{3xz+x+z}$
$z\neq 0\text{ and }x\neq 0\text{ and }\left(z=-\frac{1}{3}\text{ or }x\neq -\frac{z}{3z+1}\right)$

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 $x,y,z$.

$$xyz-yz\times 2x+xyz-xz\times 2y+xyz-xy\times 2z=yz+xz+xy$$

Combine $xyz$ and $xyz$ to get $2xyz$.

$$2xyz-yz\times 2x-xz\times 2y+xyz-xy\times 2z=yz+xz+xy$$

Combine $-yz\times 2x$ and $-xz\times 2y$ to get $2\left(-yz\times 2x\right)$.

$$2xyz+2\left(-yz\times 2x\right)+xyz-xy\times 2z=yz+xz+xy$$

Combine $2xyz$ and $xyz$ to get $3xyz$.

$$3xyz+2\left(-yz\times 2x\right)-xy\times 2z=yz+xz+xy$$

Combine $2\left(-yz\times 2x\right)$ and $-xy\times 2z$ to get $3\left(-yz\times 2x\right)$.

$$3xyz+3\left(-yz\times 2x\right)=yz+xz+xy$$

Subtract $yz$ from both sides.

$$3xyz+3\left(-yz\times 2x\right)-yz=xz+xy$$

Subtract $xy$ from both sides.

$$3xyz+3\left(-yz\times 2x\right)-yz-xy=xz$$

Multiply $3$ and $-1$ to get $-3$.

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

Multiply $-3$ and $2$ to get $-6$.

$$3xyz-6yzx-yz-xy=xz$$

Combine $3xyz$ and $-6yzx$ to get $-3xyz$.

$$-3xyz-yz-xy=xz$$

Combine all terms containing $y$.

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

The equation is in standard form.

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

Divide both sides by $-x-z-3zx$.

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

Dividing by $-x-z-3zx$ undoes the multiplication by $-x-z-3zx$.

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

Divide $xz$ by $-x-z-3zx$.

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

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

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