2150.21 – Reciprocal Symmetry

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

  1. −1-1

  2. −1-1

  3. 12\dfrac{1}{2}

  4. 22

  5. 33

Solution

We are given that 1−1(1−x)=1(1−x)1 - \dfrac{1}{(1 - x)} = \dfrac{1}{(1 - x)}.

Well, for any equation of the form 1−∘=∘1 - \circ = \circ , it must be that ∘=12\circ = \dfrac{1}{2}.

So 1(1−x)=12\dfrac{1}{(1 - x)} = \dfrac{1}{2}.

This leads to the equation 1−x=21 - x = 2, so x=−1x = -1. That’s (b).