Simplifying expression: $1 - \frac{1}{ (1 + a) / (1 - a)}$ Correct Answer is $a$
My attempt:
$$1 - \frac{1}{ (1 + a) / (1 - a)}= 1 - \frac{1 - a}{1 + a}  $$
multiply $(1 + a)$ on num and dem for the first term.  
$$=\frac{1 + a}{1 + a} - \frac{1 - a}{1 + a}$$
combine and subtract. 
$$=\frac{2a}{1 + a}$$
How does this simplify to $a$?

$$1 - \dfrac{1}{\dfrac{1 + a}{1 - a}} = 1 - \dfrac{1 - a}{1 + a} = \dfrac{1 + a}{1 + a} - \dfrac{1 - a}{1 + a} = \dfrac{(1 + a) - (1 - a)}{1 + a} = \dfrac{2a}{1 + a} \ne a;$$
I agree with user582949; our OP is right at the answer he/she was given is wrong.
