Solve 6/x+2/3=1/yf

$$\frac { 6 } { x } + \frac { 2 } { 3 } = \frac { 1 } { y } f$$

Solve for f

$$f=\frac{2y\left(x+9\right)}{3x}$$

$$x\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3xy, the least common multiple of x,3,y.

$$3y\times 6+3xy\times \frac{2}{3}=3x\times 1f$$

Multiply 3 and 6 to get 18.

$$18y+3xy\times \frac{2}{3}=3x\times 1f$$

Multiply 3 and \frac{2}{3} to get 2.

$$18y+2xy=3x\times 1f$$

Multiply 3 and 1 to get 3.

$$18y+2xy=3xf$$

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

$$3xf=18y+2xy$$

The equation is in standard form.

$$3xf=2xy+18y$$

Divide both sides by 3x.

$$\frac{3xf}{3x}=\frac{2y\left(x+9\right)}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$f=\frac{2y\left(x+9\right)}{3x}$$

Divide 2y\left(9+x\right) by 3x.

$$f=\frac{2y}{3}+\frac{6y}{x}$$

Solve for x

$$x=-\frac{18y}{2y-3f}$$

$$y\neq 0\text{ and }y\neq \frac{3f}{2}$$

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 3xy, the least common multiple of x,3,y.

$$3y\times 6+3xy\times \frac{2}{3}=3x\times 1f$$

Multiply 3 and 6 to get 18.

$$18y+3xy\times \frac{2}{3}=3x\times 1f$$

Multiply 3 and \frac{2}{3} to get 2.

$$18y+2xy=3x\times 1f$$

Multiply 3 and 1 to get 3.

$$18y+2xy=3xf$$

Subtract 3xf from both sides.

$$18y+2xy-3xf=0$$

Subtract 18y from both sides. Anything subtracted from zero gives its negation.

$$2xy-3xf=-18y$$

Combine all terms containing x.

$$\left(2y-3f\right)x=-18y$$

Divide both sides by 2y-3f.

$$\frac{\left(2y-3f\right)x}{2y-3f}=-\frac{18y}{2y-3f}$$

Dividing by 2y-3f undoes the multiplication by 2y-3f.

$$x=-\frac{18y}{2y-3f}$$

Variable x cannot be equal to 0.

$$x=-\frac{18y}{2y-3f}\text{, }x\neq 0$$