Solve 3/x+6/x-1/y=11

$$\frac { 3 } { x } + \frac { 6 } { x } - \frac { 1 } { y } = 11$$

Solve for y

$$y=\frac{x}{9-11x}$$

$$x\neq 0\text{ and }x\neq \frac{9}{11}$$

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.

$$y\times 3+y\times 6-x=11xy$$

Combine y\times 3 and y\times 6 to get 9y.

$$9y-x=11xy$$

Subtract 11xy from both sides.

$$9y-x-11xy=0$$

Add x to both sides. Anything plus zero gives itself.

$$9y-11xy=x$$

Combine all terms containing y.

$$\left(9-11x\right)y=x$$

Divide both sides by 9-11x.

$$\frac{\left(9-11x\right)y}{9-11x}=\frac{x}{9-11x}$$

Dividing by 9-11x undoes the multiplication by 9-11x.

$$y=\frac{x}{9-11x}$$

Variable y cannot be equal to 0.

$$y=\frac{x}{9-11x}\text{, }y\neq 0$$

Solve for x

$$x=\frac{9y}{11y+1}$$

$$y\neq 0\text{ and }y\neq -\frac{1}{11}$$