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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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?  [#permalink]

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21 Aug 2016, 00:04
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:51) correct 24% (02:16) wrong based on 147 sessions

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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.

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7424 Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? [#permalink] ### Show Tags 21 Aug 2016, 00:46 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 _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7101 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? [#permalink] ### Show Tags 22 Aug 2016, 19:50 If we solve the question, we get x=±√2. _________________ 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$149 for 3 month Online Course"
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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, 09:14
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 ?
Manager
Joined: 19 Jul 2017
Posts: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
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, 08:24
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
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Location: India
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, 23:12
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

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Joined: 04 Apr 2018
Posts: 21
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, 11:58
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: 13
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, 07:02
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?   [#permalink] 28 Oct 2018, 07:02
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