Last visit was: 25 Apr 2026, 10:04 It is currently 25 Apr 2026, 10:04
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
655-705 (Hard)|   Algebra|      
User avatar
delta23
User avatar
Joined: 23 Jul 2017
Last visit: 15 Mar 2022
Posts: 27
Own Kudos:
34
 [10]
Given Kudos: 213
Location: United Arab Emirates
Concentration: Finance, Entrepreneurship
WE:Analyst (Commercial Banking)
Posts: 27
Kudos: 34
 [10]
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 00:34
1
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

65% (02:44) correct 35% (02:37) wrong based on 277 sessions

History

Date
Time
Result
Not Attempted Yet
If x is an integer and \(\frac{x}{2(x−1)}\)+\(\frac{2}{x+1}\)=\(\frac{2x}{1+x}\)+\(\frac{1}{2(1−x)}\), what is the value of x?


A) -3

B) -1

C) 0

D) 2

E) 3
ShowHide Answer
Official Answer
E
User avatar
PKN
User avatar
Joined: 01 Oct 2017
Last visit: 11 Oct 2025
Posts: 809
Own Kudos:
1,637
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 809
Kudos: 1,637
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 00:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
delta23
If x is an integer and \(\frac{x}{2(x−1)}\)+\(\frac{2}{x+1}\)=\(\frac{2x}{1+x}\)+\(\frac{1}{2(1−x)}\), what is the value of x?


A) -3

B) -1

C) 0

D) 2

E) 3
Show more

\(\frac{x}{2(x−1)}\)+\(\frac{2}{x+1}\)=\(\frac{2x}{1+x}\)+\(\frac{1}{2(1−x)}\)
Or, \(\frac{x(x+1)+4(x-1)}{2(x+1)(x-1)}=\frac{4x(1-x)+(1+x)}{2(1+x)(1-x)}\)
Or, \(\frac{x^2+5x-4}{2(x+1)(x-1)}= \frac{-4x^2+5x+1}{-2(x+1)(x-1)}\)
Or,\(x^2+5x-4=-(-4x^2+5x+1)\)
Or, \(x^2+5x-4=4x^2-5x-1\)
Or, \(3x^2-9x-x+3=0\)
Or, 3x(x-3)-1(x-3)=0
Or, (x-3)(3x-1)=0
Or, x=3 or, x=\(\frac{1}{3}\)

Given,x is an integer. Hence, x=3.

Ans. (E)
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,442
Own Kudos:
79,411
 [4]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,442
Kudos: 79,411
 [4]
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 01:05
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
delta23
If x is an integer and \(\frac{x}{2(x−1)}\)+\(\frac{2}{x+1}\)=\(\frac{2x}{1+x}\)+\(\frac{1}{2(1−x)}\), what is the value of x?


A) -3

B) -1

C) 0

D) 2

E) 3
Show more

\(\frac{x}{2(x−1)}+\frac{2}{x+1}=\frac{2x}{1+x}+\frac{1}{2(1−x)}\)

Plugging in options would be my first choice here. Not a lot of work is required to try x = 0 since some terms become 0.
x cannot be -1 since we can't have 0 in the denominator.
2 is possible option but that doesn't work.
Try x = 3 and it fits.

Answer (E)

Note that you can simplify the terms by bringing the common terms together and then plug in but as it is too it is not cumbersome.
avatar
ColumbiaEMBA
avatar
Joined: 29 Sep 2017
Last visit: 24 Mar 2019
Posts: 88
Own Kudos:
61
 [1]
Given Kudos: 10
Location: United States
Products:
My Reviews
Posts: 88
Kudos: 61
 [1]
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 01:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
delta23
KarishmaB Bunuel, please help
Show more

Easiest way to do it is to plug answer choices in and see which one works. Only E works.
avatar
WIKI18
avatar
Joined: 27 Jun 2018
Last visit: 15 May 2020
Posts: 22
Own Kudos:
24
Given Kudos: 37
Location: Pakistan
Posts: 22
Kudos: 24
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 04:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Would there be a way to solve this in under 2 minutes?

I tried simplifying the equation to reach the answer and it took me approx. 7 minutes to do so.

Thanks!
User avatar
Princ
User avatar
Joined: 22 Feb 2018
Last visit: 04 May 2025
Posts: 351
Own Kudos:
925
 [2]
Given Kudos: 34
Posts: 351
Kudos: 925
 [2]
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 05:16
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
WIKI18
Would there be a way to solve this in under 2 minutes?

I tried simplifying the equation to reach the answer and it took me approx. 7 minutes to do so.

Thanks!
Show more

OA: E

\(\frac{x}{2(x-1)}+\frac{2}{x+1}=\frac{2x}{1+x}+\frac{1}{2(1-x)}\)

Multiplying both sides by \(2(x-1)(x+1)\),we get

\(x(x+1)+4(x-1)=4x(x-1)-(x+1)\)

\(x^2+x+4x-4=4x^2-4x-x-1\)

\(3x^2 -10x+3=0\)
\(3x^2 -9x-1x+3=0\)
\(3x(x-3)-1(x-3)=0\)
\((3x-1)(x-3)=0\)
\(x=\frac{1}{3}\)(Rejected as \(x\) should be an integer), \(3\)
\(x=3\)
avatar
WIKI18
avatar
Joined: 27 Jun 2018
Last visit: 15 May 2020
Posts: 22
Own Kudos:
24
Given Kudos: 37
Location: Pakistan
Posts: 22
Kudos: 24
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 05:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Princ
WIKI18
Would there be a way to solve this in under 2 minutes?

I tried simplifying the equation to reach the answer and it took me approx. 7 minutes to do so.

Thanks!

OA: E

\(\frac{x}{2(x-1)}+\frac{2}{x+1}=\frac{2x}{1+x}+\frac{1}{2(1-x)}\)

Multiplying both sides by \(2(x-1)(x+1)\),we get

\(x(x+1)+4(x-1)=4x(x-1)-(x+1)\)

\(x^2+x+4x-4=4x^2-4x-x-1\)

\(3x^2 -10x+3=0\)
\(3x^2 -9x-1x+3=0\)
\(3x(x-3)-1(x-3)=0\)
\((3x-1)(x-3)=0\)
\(x=\frac{1}{3}\)(Rejected as \(x\) should be an integer), \(3\)
\(x=3\)
Show more

When I multiply the last term i.e. \(\frac{1}{2(1-x)}\) by \(2(x-1)(x+1)\) I get \(\frac{(x-1)(x+1)}{(1-x)}\)

Can you please explain how you reached\((x+1)\)?
User avatar
Princ
User avatar
Joined: 22 Feb 2018
Last visit: 04 May 2025
Posts: 351
Own Kudos:
925
 [1]
Given Kudos: 34
Posts: 351
Kudos: 925
 [1]
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 07:00
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WIKI18
Princ
WIKI18
Would there be a way to solve this in under 2 minutes?

I tried simplifying the equation to reach the answer and it took me approx. 7 minutes to do so.

Thanks!

OA: E

\(\frac{x}{2(x-1)}+\frac{2}{x+1}=\frac{2x}{1+x}+\frac{1}{2(1-x)}\)

Multiplying both sides by \(2(x-1)(x+1)\),we get

\(x(x+1)+4(x-1)=4x(x-1)-(x+1)\)

\(x^2+x+4x-4=4x^2-4x-x-1\)

\(3x^2 -10x+3=0\)
\(3x^2 -9x-1x+3=0\)
\(3x(x-3)-1(x-3)=0\)
\((3x-1)(x-3)=0\)
\(x=\frac{1}{3}\)(Rejected as \(x\) should be an integer), \(3\)
\(x=3\)

When I multiply the last term i.e. \(\frac{1}{2(1-x)}\) by \(2(x-1)(x+1)\) I get \(\frac{(x-1)(x+1)}{(1-x)}\)

Can you please explain how you reached\((x+1)\)?
Show more
WIKI18
\(2(x-1)(x+1)\)*\(\frac{1}{2(1-x)}\)=\(2(x-1)(x+1)\)*\(\frac{1}{-2(x-1)}\) =\((x+1)\)*\(-1=-(x+1)\)
Let me know if further explaination is required.
avatar
WIKI18
avatar
Joined: 27 Jun 2018
Last visit: 15 May 2020
Posts: 22
Own Kudos:
24
Given Kudos: 37
Location: Pakistan
Posts: 22
Kudos: 24
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 05 Aug 2018, 07:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Princ


\(2(x-1)(x+1)\)*\(\frac{1}{2(1-x)}\)=\(2(x-1)(x+1)\)*\(\frac{1}{-2(x-1)}\) =\((x+1)\)*\(-1=-(x+1)\)
Let me know if further explaination is required.
Show more

Got it now. Thanks!
User avatar
ZIX
User avatar
Joined: 30 Sep 2023
Last visit: 22 Jan 2026
Posts: 89
Own Kudos:
178
Given Kudos: 526
Posts: 89
Kudos: 178
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 08 Mar 2024, 23:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Here is an easier approach:
  • \(\frac{x}{2x-2}­\)­ + \(\frac{2}{x+1}­\)­ = \(\frac{2x}{x+1}­\)­ + \(\frac{1}{2-2x}­\)­
  • \(\frac{x}{2x-2}­\)­ - \(\frac{1}{2-2x}­\)­ = \(\frac{2x}{x+1}­\)­ - \(\frac{2}{x+1}­\)­
  • \(\frac{x}{2x-2}­\)­ - \((\frac{-1}{2x-2}­)\)­ = \(\frac{2x - 2}{x+1}­\)
  • \(\frac{x+1}{2x-2}­\)­ = \(\frac{2x - 2}{x+1}­\)
  • \((x+1)^2 = (2x-2)^2\)
solve the quadratic and you get x = 3 or 1/3
 ­
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,986
Own Kudos:
1,117
Posts: 38,986
Kudos: 1,117
If x is an integer and x2(x−1)+2x+1=2x1+x+12(1−x) 11 May 2025, 03:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109827 posts
Krunaal
Tuck School Moderator
852 posts