Solve x/x-4+4m/4-x=2m

$$\frac { x } { x - 4 } + \frac { 4 m } { 4 - x } = 2 m$$

Solve for m

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x-4, the least common multiple of x-4,4-x.

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

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

$$x-4m=2mx-8m$$

Subtract 2mx from both sides.

$$x-4m-2mx=-8m$$

Add 8m to both sides.

$$x-4m-2mx+8m=0$$

Combine -4m and 8m to get 4m.

$$x+4m-2mx=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$4m-2mx=-x$$

Combine all terms containing m.

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

Divide both sides by 4-2x.

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

Dividing by 4-2x undoes the multiplication by 4-2x.

$$m=-\frac{x}{4-2x}$$

Divide -x by 4-2x.

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

Solve for x

$$x=-\frac{4m}{1-2m}$$

$$m\neq 1\text{ and }m\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4, the least common multiple of x-4,4-x.

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

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

$$x-4m=2mx-8m$$

Subtract 2mx from both sides.

$$x-4m-2mx=-8m$$

Add 4m to both sides.

$$x-2mx=-8m+4m$$

Combine -8m and 4m to get -4m.

$$x-2mx=-4m$$

Combine all terms containing x.

$$\left(1-2m\right)x=-4m$$

Divide both sides by 1-2m.

$$\frac{\left(1-2m\right)x}{1-2m}=-\frac{4m}{1-2m}$$

Dividing by 1-2m undoes the multiplication by 1-2m.

$$x=-\frac{4m}{1-2m}$$

Variable x cannot be equal to 4.

$$x=-\frac{4m}{1-2m}\text{, }x\neq 4$$