How to solve (6)/(x)-(2)/(y)=1

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 (6)/(x)-(2)/(y)=1 | Equatix

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Question

$$\frac{ 6 }{ x } - \frac{ 2 }{ y } =1$$

Solve for x

$x=\frac{6y}{y+2}$
$y\neq 0\text{ and }y\neq -2$

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 $x,y$.

$$y\times 6-x\times 2=xy$$

Subtract $xy$ from both sides.

$$y\times 6-x\times 2-xy=0$$

Subtract $y\times 6$ from both sides. Anything subtracted from zero gives its negation.

$$-x\times 2-xy=-y\times 6$$

Multiply $-1$ and $2$ to get $-2$.

$$-2x-xy=-y\times 6$$

Multiply $-1$ and $6$ to get $-6$.

$$-2x-xy=-6y$$

Combine all terms containing $x$.

$$\left(-2-y\right)x=-6y$$

The equation is in standard form.

$$\left(-y-2\right)x=-6y$$

Divide both sides by $-2-y$.

$$\frac{\left(-y-2\right)x}{-y-2}=-\frac{6y}{-y-2}$$

Dividing by $-2-y$ undoes the multiplication by $-2-y$.

$$x=-\frac{6y}{-y-2}$$

Divide $-6y$ by $-2-y$.

$$x=\frac{6y}{y+2}$$

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

$$x=\frac{6y}{y+2}\text{, }x\neq 0$$

Show Solution

Solve for y

$y=-\frac{2x}{x-6}$
$x\neq 0\text{ and }x\neq 6$

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 $x,y$.

$$y\times 6-x\times 2=xy$$

Subtract $xy$ from both sides.

$$y\times 6-x\times 2-xy=0$$

Add $x\times 2$ to both sides. Anything plus zero gives itself.

$$y\times 6-xy=x\times 2$$

Combine all terms containing $y$.

$$\left(6-x\right)y=x\times 2$$

The equation is in standard form.

$$\left(6-x\right)y=2x$$

Divide both sides by $6-x$.

$$\frac{\left(6-x\right)y}{6-x}=\frac{2x}{6-x}$$

Dividing by $6-x$ undoes the multiplication by $6-x$.

$$y=\frac{2x}{6-x}$$

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

$$y=\frac{2x}{6-x}\text{, }y\neq 0$$

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