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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6495 GMAT 1: 760 Q51 V42 GPA: 3.82 If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? [#permalink] ### Show Tags 20 Aug 2016, 23:04 00:00 Difficulty: 25% (medium) Question Stats: 74% (01:41) correct 26% (01:29) wrong based on 134 sessions ### HideShow timer Statistics If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? A. √2 B. ±√2 C. 1 D. 2 E. √5 *An answer will be posted in 2 days. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Posts: 7022
Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  [#permalink]

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20 Aug 2016, 23:46
MathRevolution wrote:
If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?
A. √2
B. ±√2
C. 1
D. 2
E. √5

*An answer will be posted in 2 days.

Hi,

two ways to do it..

1) substitute value
when you substitute value of x as √2 , we get the required answer, BUT the value √2 is also in B..
check for -√2 , you will get answer as B..

2) proper method
$$\frac{1}{x(x+1)}+\frac{1}{(x+1)(x+2)}=\frac{1}{(x+1)}$$....
$$\frac{1}{(x+1)}(\frac{1}{x}+\frac{1}{(x+2)}-1)=0$$....
so either \frac{1}{(x+1)}=0, that is not posible as numerator cannot be 0..
so $$(\frac{1}{x}+\frac{1}{(x+2)}-1)=0......\frac{x+2+x-x^2-2x}{x(x+2)}=0$$....
$$x+2+x-x^2-2x=0........x^2=2....$$or x= ±√2
B
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Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  [#permalink]

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22 Aug 2016, 18:50
If we solve the question, we get x=±√2.
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Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  [#permalink]

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23 Aug 2016, 08:14
MathRevolution wrote:
If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?
A. √2
B. ±√2
C. 1
D. 2
E. √5

*An answer will be posted in 2 days.

This is a straight algebraic equation with no catch. How come listed as 600-700 category question ?
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Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  [#permalink]

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17 Sep 2017, 07:24
MathRevolution wrote:
If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?
A. √2
B. ±√2
C. 1
D. 2
E. √5

*An answer will be posted in 2 days.

From the Question stem cancel out the common denominator x+1;

so it becomes (1/x)+(1/x+2)=1;

Solving this we get x+2+x = x(x+2);

2x+2=x^+2x
so x= ±√2
Ans:B
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Joined: 09 Mar 2018
Posts: 24
If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  [#permalink]

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18 Oct 2018, 22:12
Given : 1/x(x+1) + 1/((x+1)(x+2))=1/(x+1)

Take the LCM in LHS, making the LHS as

$$\frac{2x+2}{x*(x+1)* (x+2)}$$ = $$\frac{1}{x+1}$$

Now if you cross multiply the denominator of LHS to RHS

Equation will be reduced to

2x + 2 = x^2 + 2x

$$x^2$$ = 2

Giving answer as B
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Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  [#permalink]

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20 Oct 2018, 10:58
does the Gmat presents fractions in this way?
the majority of the time in this Qs I only had to make sure I wrote the equation right....
Intern
Joined: 10 Oct 2017
Posts: 11
Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  [#permalink]

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28 Oct 2018, 06:02
does the Gmat presents fractions in this way?
the majority of the time in this Qs I only had to make sure I wrote the equation right....

I don't think GMAT would expect us to waste time in checking the question.
It'll be straightforward most of the time. Not to worry much about that.
Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? &nbs [#permalink] 28 Oct 2018, 06:02
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# If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?

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