Solve xdiv(z-3)-xdivz=2

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

Solve for x

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

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

Steps for Solving Linear Equation

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

$$zx-\left(z-3\right)x=2z\left(z-3\right)$$

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

$$zx-\left(zx-3x\right)=2z\left(z-3\right)$$

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

$$zx-zx+3x=2z\left(z-3\right)$$

Combine zx and -zx to get 0.

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

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

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

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Solve for z

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

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