Solve 5+m/x-2+1=1/x-2

$$\frac{ 5+m }{ x-2 } +1 = \frac{ 1 }{ x-2 }$$

Solve for m

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

$$x\neq 2$$

Solution Steps

Multiply both sides of the equation by x-2.

$$5+m+x-2=1$$

Subtract 2 from 5 to get 3.

$$3+m+x=1$$

Subtract 3 from both sides.

$$m+x=1-3$$

Subtract 3 from 1 to get -2.

$$m+x=-2$$

Subtract x from both sides.

$$m=-2-x$$

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.

$$5+m+x-2=1$$

Subtract 2 from 5 to get 3.

$$3+m+x=1$$

Subtract 3 from both sides.

$$m+x=1-3$$

Subtract 3 from 1 to get -2.

$$m+x=-2$$

Subtract m from both sides.

$$x=-2-m$$

Variable x cannot be equal to 2.

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