Simplifying expression: $1 - \frac{1}{ (1 + a) / (1 - a)}$

Question

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 $a$?

You should format your questions using MathJax if you want a quick answer :) — Matt, Aug 10 '18 at 16:12
I don't know why anyone would think the answer is $a$, but you've correctly solved the problem as you've stated it. — J.G., Aug 10 '18 at 16:13
Thanks. The solution manual just stated the answer without a solution. — user9995331, Aug 10 '18 at 16:14

score 3 · Answer 1 · answered Aug 10 '18 at 16:12

3

$$1 - {1\over {1 + a\over 1 - a}} = 1-{1-a\over 1+a} ={1+a\over 1+a}- {1-a\over 1+a} = {2a\over 1+a}$$

so it does not. Your calculations are correct.

answered Aug 10 '18 at 16:12

score 2 · Answer 2 · answered Aug 10 '18 at 16:17

$$1 - \dfrac{1}{\dfrac{1 + a}{1 - a}} = 1 - \dfrac{1 - a}{1 + a} = \dfrac{1 + a}{1 + a} - \dfrac{1 - a}{1 + a} = \dfrac{(1 + a) - (1 - a)}{1 + a} = \dfrac{2a}{1 + a} \ne a;$$

I agree with user582949; our OP is right at the answer he/she was given is wrong.

Simplifying expression: $1 - \frac{1}{ (1 + a) / (1 - a)}$

2 Answers2