Math Destroyer 2011 Test #12 Question #28 need help!!

[toothhornet88]

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Simplify the expression as much as possible (where "a" doesn't equal to 1)

1-1/[1+a/(1-a)]

The answer is "a" but i keep getting "-a" Please tell me what am I doing wrong?

Thanks a lot in advance

 

[FROGGBUSTER]

Simplify the expression as much as possible (where "a" doesn't equal to 1)

1-1/[1+a/(1-a)]

The answer is "a" but i keep getting "-a" Please tell me what am I doing wrong?

Thanks a lot in advance

I have a feeling you're treating (1+a) as a numerator. It should be 1 + [a / (1-a)] in the denominator there.

 

[toothhornet88]

I have a feeling you're treating (1+a) as a numerator. It should be 1 + [a / (1-a)] in the denominator there.

Well this is how I solved it:

https://dl-web.dropbox.com/get/Screen shot 2011-07-19 at 7.52.33 AM.png?w=b4f05b8c

 

[NewBee12]

I think I know what are you doing wrong.
This is what you get after the first step: 1-[1/1/(1-a)] which is 1-(1-a). I think you didn't distribute the minus sign.
The answer is a

 

[toothhornet88]

I think I know what are you doing wrong.
This is what you get after the first step: 1-[1/1/(1-a)] which is 1-(1-a). I think you didn't distribute the minus sign.
The answer is a

I see. I just thought 1-(1-a) is same as 1-1-a

 

[juusstin]

I was stuck on this problem too and came across this thread would anybody be kind enough to explain to me what to do in the first step to get 1-[1/1/(1-a)] mentioned by newbee12?

Thanks

 

[crax]

So the problem is setup as so:

1 - 1 / ( 1 + a/[1-a])
which also reads as

1 - 1 / ( 1 + {a/[1-a]}) implying the denominator of 1-a does not apply to the first "1" within the parenthesis.

Ignoring the first term for a moment, let us focus on the second term

1
-------------------
1 + a /(1-a)

We dont like the denominator within the denominator here, so lets cancel it out by multiplying the whole denominator by 1-a. To make sure we are not changing the equation, we also must multiply the numerator by 1-a, in essence multiplying the whole term by (1-a)/(1-a) which is = to 1, hence not "changing" the problem.

1 (1-a)
-------------------
[1 + a /(1-a)] [1-a] (make sure to multiply the [1-a] to both the first and second term within the bracket

1-a
-----------
(1-a) + a
reduces to
1-a
-----
1-a+a=1

reduces to 1-a. Now, you can go ahead and plug back into the original equation

1 - 1 / ( 1 + a/[1-a]) where we have simplified the second term to (1-a) /1.
1 - (1-a)
Distribute the negative
1-1+a
0+a
a

 

[C0LA]

bump! Would somebody mind writing out the algebra on paper and then uploading a picture? Still not quite understanding the explanations above. Thank you!