2150.21 – Reciprocal Symmetry

If one minus the reciprocal of (1 - x) equals the reciprocal of (1 - x), then what is x?

  1. -1
  2. -1
  3. 1/2
  4. 2
  5. 3
Solution

We are given that 1 - 1/(1 - x) = 1/(1 - x).

Well, for any equation of the form 1 - \circ = \circ , it must be that \circ = 1/2.

So 1/(1-x) = 1/2.

This leads to the equation 1 - x = 2, so x = -1. That’s (b).