Solve xdiv(y-3)-xdivy=2

$$x \div (y-3)-x \div y=2$$

Solve for x

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by y\left(y-3\right), the least common multiple of y-3,y.

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

Use the distributive property to multiply y-3 by x.

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

To find the opposite of yx-3x, find the opposite of each term.

$$yx-yx+3x=2y\left(y-3\right)$$

Combine yx and -yx to get 0.

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

Use the distributive property to multiply 2y by y-3.

$$3x=2y^{2}-6y$$

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Solve for y (complex solution)

$$y=\frac{-\sqrt{6x+9}+3}{2}$$

$$y=\frac{\sqrt{6x+9}+3}{2}\text{, }x\neq 0$$

Solve for y

$$y=\frac{-\sqrt{6x+9}+3}{2}$$

$$y=\frac{\sqrt{6x+9}+3}{2}\text{, }x\neq 0\text{ and }x\geq -\frac{3}{2}$$