Solve m/x-2-2x/2-x=1

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

Solve for m

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

$$x\neq 2$$

Solution Steps

Multiply both sides of the equation by x-2, the least common multiple of x-2,2-x.

$$m+2x=x-2$$

Subtract 2x from both sides.

$$m=x-2-2x$$

Combine x and -2x to get -x.

$$m=-x-2$$

Solve for x

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

$$m\neq -4$$

Solution Steps

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2, the least common multiple of x-2,2-x.

$$m+2x=x-2$$

Subtract x from both sides.

$$m+2x-x=-2$$

Combine 2x and -x to get x.

$$m+x=-2$$

Subtract m from both sides.

$$x=-2-m$$

Variable x cannot be equal to 2.

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