Solve m/x-1+3/1-x=1

$$\frac { m } { x - 1 } + \frac { 3 } { 1 - x } = 1$$

Solve for m

$$m=x+2$$

$$x\neq 1$$

Solution Steps

Multiply both sides of the equation by x-1, the least common multiple of x-1,1-x.

$$m-3=x-1$$

Add 3 to both sides.

$$m=x-1+3$$

Add -1 and 3 to get 2.

$$m=x+2$$

Solve for x

$$x=m-2$$

$$m\neq 3$$

Solution Steps

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1, the least common multiple of x-1,1-x.

$$m-3=x-1$$

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

$$x-1=m-3$$

Add 1 to both sides.

$$x=m-3+1$$

Add -3 and 1 to get -2.

$$x=m-2$$

Variable x cannot be equal to 1.

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