Solve 1/x+3/y=9

$$\frac{ 1 }{ x } + \frac{ 3 }{ y } =9$$

Solve for x

$$x=-\frac{y}{3\left(1-3y\right)}$$

$$y\neq 0\text{ and }y\neq \frac{1}{3}$$

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.

$$y+x\times 3=9xy$$

Subtract 9xy from both sides.

$$y+x\times 3-9xy=0$$

Subtract y from both sides. Anything subtracted from zero gives its negation.

$$x\times 3-9xy=-y$$

Combine all terms containing x.

$$\left(3-9y\right)x=-y$$

Divide both sides by 3-9y.

$$\frac{\left(3-9y\right)x}{3-9y}=-\frac{y}{3-9y}$$

Dividing by 3-9y undoes the multiplication by 3-9y.

$$x=-\frac{y}{3-9y}$$

Divide -y by 3-9y.

$$x=-\frac{y}{3\left(1-3y\right)}$$

Variable x cannot be equal to 0.

$$x=-\frac{y}{3\left(1-3y\right)}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{3x}{1-9x}$$

$$x\neq 0\text{ and }x\neq \frac{1}{9}$$

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.

$$y+x\times 3=9xy$$

Subtract 9xy from both sides.

$$y+x\times 3-9xy=0$$

Subtract x\times 3 from both sides. Anything subtracted from zero gives its negation.

$$y-9xy=-x\times 3$$

Multiply -1 and 3 to get -3.

$$y-9xy=-3x$$

Combine all terms containing y.

$$\left(1-9x\right)y=-3x$$

Divide both sides by 1-9x.

$$\frac{\left(1-9x\right)y}{1-9x}=-\frac{3x}{1-9x}$$

Dividing by 1-9x undoes the multiplication by 1-9x.

$$y=-\frac{3x}{1-9x}$$

Variable y cannot be equal to 0.

$$y=-\frac{3x}{1-9x}\text{, }y\neq 0$$