Solve x/x-2=2-m/2x

$$\frac { x } { x - 2 } = 2 - \frac { m } { 2 x }$$

Solve for m

$$m=-\frac{2x\left(4-x\right)}{x-2}$$

$$x\neq 2\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x\left(x-2\right), the least common multiple of x-2,2x.

$$2xx=2x\left(x-2\right)\times 2-\left(x-2\right)m$$

Multiply x and x to get x^{2}.

$$2x^{2}=2x\left(x-2\right)\times 2-\left(x-2\right)m$$

Multiply 2 and 2 to get 4.

$$2x^{2}=4x\left(x-2\right)-\left(x-2\right)m$$

Use the distributive property to multiply 4x by x-2.

$$2x^{2}=4x^{2}-8x-\left(x-2\right)m$$

Use the distributive property to multiply x-2 by m.

$$2x^{2}=4x^{2}-8x-\left(xm-2m\right)$$

To find the opposite of xm-2m, find the opposite of each term.

$$2x^{2}=4x^{2}-8x-xm+2m$$

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

$$4x^{2}-8x-xm+2m=2x^{2}$$

Subtract 4x^{2} from both sides.

$$-8x-xm+2m=2x^{2}-4x^{2}$$

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$-8x-xm+2m=-2x^{2}$$

Add 8x to both sides.

$$-xm+2m=-2x^{2}+8x$$

Combine all terms containing m.

$$\left(-x+2\right)m=-2x^{2}+8x$$

The equation is in standard form.

$$\left(2-x\right)m=8x-2x^{2}$$

Divide both sides by -x+2.

$$\frac{\left(2-x\right)m}{2-x}=\frac{2x\left(4-x\right)}{2-x}$$

Dividing by -x+2 undoes the multiplication by -x+2.

$$m=\frac{2x\left(4-x\right)}{2-x}$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{\sqrt{m^{2}+64}+m+8}{4}\text{, }&\text{unconditionally}\\x=\frac{-\sqrt{m^{2}+64}+m+8}{4}\text{, }&m\neq 0\end{matrix}\right.$$