Solve a rational equation and keep its restriction

Work through it

1. 1

   x ≠ 1

   The original denominator cannot be zero, so exclude x = 1 before solving.

2. 2

   1 = 2(x - 1)

   Multiply both sides by x - 1, which is allowed because the restriction says it is nonzero.

3. 3

   1 = 2x - 2, so 3 = 2x

   Distribute 2, then add 2 to both sides to isolate the x-term.

4. 4

   x = 3/2

   Divide by 2. This value is not the excluded value 1, so it is valid in the original equation.