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

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

Solve for x

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

$$m\neq 4\text{ and }m\neq 2$$

Steps for Solving Linear Equation

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

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

Multiply 2 and 2 to get 4.

$$4x+\left(m-2\right)m=x\times 2\left(m-2\right)$$

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

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

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

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

Multiply -2 and 2 to get -4.

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

Subtract 2xm from both sides.

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

Add 4x to both sides.

$$4x+m^{2}-2m-2xm+4x=0$$

Combine 4x and 4x to get 8x.

$$8x+m^{2}-2m-2xm=0$$

Subtract m^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add 2m to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 8-2m.

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

Dividing by 8-2m undoes the multiplication by 8-2m.

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

Divide m\left(2-m\right) by 8-2m.

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

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=-\sqrt{x^{2}-6x+1}+x+1\text{, }&\text{unconditionally}\\m=\sqrt{x^{2}-6x+1}+x+1\text{, }&x\neq 0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=-\sqrt{x^{2}-6x+1}+x+1\text{, }&x\geq 2\sqrt{2}+3\text{ or }x\leq 3-2\sqrt{2}\\m=\sqrt{x^{2}-6x+1}+x+1\text{, }&x\geq 2\sqrt{2}+3\text{ or }\left(x\neq 0\text{ and }x\leq 3-2\sqrt{2}\right)\end{matrix}\right.$$