If $f(a) = \frac{1}{1-a}$, find the product $f^{-1}(a) \times a \times f(a)$.  (Assume $a \neq 0$ and $a \neq 1$.)
Question:
If $f(a) = \frac{1}{1-a}$, find the product $f^{-1}(a) \times a \times f(a)$.  (Assume $a \neq 0$ and $a \neq 1$.)
Answer:
Let's think step by step.

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If $f(a) = \frac{1}{1-a}$, find the product $f^{-1}(a) \times a \times f(a)$.  (Assume $a \neq 0$ and $a \neq 1$.)
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