Pls help me out with this question!!
Given, (x+1/x -1)^2
If x not equal to 0, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?
[answer choices are in the image, sorry will take too long to type them all out! lol ]
This is what I've done so far, dunno how to simplify beyond a point....
(x+1/x -1)^2 become [(1/x + 1)/(1/x -1)]^2 => [(1+x/x) / (1-x/x) ] ^2
=> [1+x / x * x/1-x ] ^2 => [(1 +x)/(1-x)]^2 => NOW WHAT?
How do i manipulate [(1+x)/(1-x)]^2 to become one of the answer choices????? HELP!
btw answer is A.
if x not equal to 0, and if x is replaced by 1/x everywhere
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You got [(1 +x)/(1-x)]^2
Then we can write (1-x)^2 = (x-1)^2, since we are squaring so both (1-x)^2 and (x-1)^2 will give same values.
Hence, [(1+x)/(1-x)]^2 = [(x+1)/(x-1)]^2
The correct answer is (A).
Hope this helps?
Then we can write (1-x)^2 = (x-1)^2, since we are squaring so both (1-x)^2 and (x-1)^2 will give same values.
Hence, [(1+x)/(1-x)]^2 = [(x+1)/(x-1)]^2
The correct answer is (A).
Hope this helps?
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Hey, that works!! cool that's something i didn't notice before that (1-x)^2 & (x-1)^2 give the same values! tried it on the numerator too...will def come in handy! thanks!!!Rahul@gurome wrote:You got [(1 +x)/(1-x)]^2
Then we can write (1-x)^2 = (x-1)^2, since we are squaring so both (1-x)^2 and (x-1)^2 will give same values.
Hence, [(1+x)/(1-x)]^2 = [(x+1)/(x-1)]^2
The correct answer is (A).
Hope this helps?
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This is #208 from the OG 12th edition. The official answer is A. Solution attached. If you can't see the attachment, see it here.
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thanks! i have the og companion i'm a BIG fan of it but this one is not explained in much detail or at least I didn't get it! thanks though!Patrick_GMATFix wrote:This is #208 from the OG 12th edition. The official answer is A. Solution attached. If you can't see the attachment, see it here.
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Thx for the feedback
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Let's give it a shot! Let's keep it simple with x = 2kwhite wrote:is it possible to solve this by picking numbers?
From the original equation, we get 9
When replacing 2 with 1/2, we get
[(3/2)/(-1/2)]^2 = 9
Obviously A works
B is the recipcrocal of A -> 1/9
C gives (5/4)/(3/4) = 5/3
D gives (-3/4)/(5/4) = -3/5
E is just the negative of B -> -1/9
A is the answer...no algebra needed
Thank you for your quick reply, but I guess my confusion comes in because I don't understand how we can decipher from the question that we are to plug 1/x into the solution part. I understand switching X --> 1/x in the example equation but shouldn't we use X for the answer choices when picking numbers? because we are trying to match the original equation with "1/x" to an answer with "x"? so confused because i don't see where it says to match sub 1/x into the answer solutions.krusta80 wrote:Let's give it a shot! Let's keep it simple with x = 2kwhite wrote:is it possible to solve this by picking numbers?
From the original equation, we get 9
When replacing 2 with 1/2, we get
[(3/2)/(-1/2)]^2 = 9
Obviously A works
B is the recipcrocal of A -> 1/9
C gives (5/4)/(3/4) = 5/3
D gives (-3/4)/(5/4) = -3/5
E is just the negative of B -> -1/9
A is the answer...no algebra needed
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You're right! I think I was looking at this problem in a weird way when I did it before. Of course, the easiest thing to do would be to substitute x = 2 into the choices. As you can see, A gives you 9 when doing so.kwhite wrote:Thank you for your quick reply, but I guess my confusion comes in because I don't understand how we can decipher from the question that we are to plug 1/x into the solution part. I understand switching X --> 1/x in the example equation but shouldn't we use X for the answer choices when picking numbers? because we are trying to match the original equation with "1/x" to an answer with "x"? so confused because i don't see where it says to match sub 1/x into the answer solutions.krusta80 wrote:Let's give it a shot! Let's keep it simple with x = 2kwhite wrote:is it possible to solve this by picking numbers?
From the original equation, we get 9
When replacing 2 with 1/2, we get
[(3/2)/(-1/2)]^2 = 9
Obviously A works
B is the recipcrocal of A -> 1/9
C gives (5/4)/(3/4) = 5/3
D gives (-3/4)/(5/4) = -3/5
E is just the negative of B -> -1/9
A is the answer...no algebra needed
Sorry for any confusion...I should have substituted x into the choices as you said.
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I found this question very odd and confusing. Because the equation that is given and the answer choice A is completely identical. I somehow talked myself out of selecting that answer, because that seems too easy. I don't know why GMAT would ask this question. Can anyone shed some light on this.mitzwillrockgmat wrote:Pls help me out with this question!!
Given, (x+1/x -1)^2
If x not equal to 0, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?
[answer choices are in the image, sorry will take too long to type them all out! lol ]
This is what I've done so far, dunno how to simplify beyond a point....
(x+1/x -1)^2 become [(1/x + 1)/(1/x -1)]^2 => [(1+x/x) / (1-x/x) ] ^2
=> [1+x / x * x/1-x ] ^2 => [(1 +x)/(1-x)]^2 => NOW WHAT?
How do i manipulate [(1+x)/(1-x)]^2 to become one of the answer choices????? HELP!
btw answer is A.
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Probably just to see if you could catch that and had the confidence to realize that the equation might be unchanged. (It does require you to do a bit of a double take, doesn't it?)Boredguy1543 wrote:I found this question very odd and confusing. Because the equation that is given and the answer choice A is completely identical. I somehow talked myself out of selecting that answer, because that seems too easy. I don't know why GMAT would ask this question. Can anyone shed some light on this.mitzwillrockgmat wrote:Pls help me out with this question!!
Given, (x+1/x -1)^2
If x not equal to 0, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?
[answer choices are in the image, sorry will take too long to type them all out! lol ]
This is what I've done so far, dunno how to simplify beyond a point....
(x+1/x -1)^2 become [(1/x + 1)/(1/x -1)]^2 => [(1+x/x) / (1-x/x) ] ^2
=> [1+x / x * x/1-x ] ^2 => [(1 +x)/(1-x)]^2 => NOW WHAT?
How do i manipulate [(1+x)/(1-x)]^2 to become one of the answer choices????? HELP!
btw answer is A.