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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None

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Manager  G
Joined: 30 May 2018
Posts: 88
GMAT 1: 620 Q42 V34 WE: Corporate Finance (Commercial Banking)
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 36% (02:09) correct 64% (02:28) wrong based on 47 sessions

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How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have?

A. None
B. 1
C. 2
D. 3
E. 5
Manager  G
Joined: 11 Feb 2013
Posts: 216
Location: United States (TX)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38 GPA: 3.05
WE: Analyst (Commercial Banking)
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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X can be √3 or -√3
X cannot be 0, -1 or -2

Posted from my mobile device

Originally posted by BelalHossain046 on 21 Mar 2019, 14:56.
Last edited by BelalHossain046 on 29 Mar 2019, 18:38, edited 1 time in total.
Manager  G
Joined: 11 Feb 2013
Posts: 216
Location: United States (TX)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38 GPA: 3.05
WE: Analyst (Commercial Banking)
Re: How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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I would go for C.
If any other short formula is available, pls share.

Posted from my mobile device
Director  V
Joined: 27 May 2012
Posts: 932
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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1
BelalHossain046 wrote:
X can 3 or -3
X cannot be 0, -1 or -2

Posted from my mobile device

You did everything correct , except in the last step
if $$x^2$$ = 3 then x=$$\pm\sqrt{3}$$

Hope this helps.
_________________
- Stne
Manager  G
Joined: 11 Feb 2013
Posts: 216
Location: United States (TX)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38 GPA: 3.05
WE: Analyst (Commercial Banking)
Re: How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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stne wrote:
BelalHossain046 wrote:
X can 3 or -3
X cannot be 0, -1 or -2

Posted from my mobile device

You did everything correct , except in the last step
if $$x^2$$ = 3 then x=$$\pm\sqrt{3}$$

Hope this helps.

Got it . thank you a lot.
Those r the mistakes that are responsible for my poor score.
Intern  B
Joined: 17 Feb 2019
Posts: 2
Re: How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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the given question is an inequality.
so if you cross multiply LHS and compare it with RHS, you can remove (x+1) from both denominators.
so now you have {x(x+2) + x(x=1)}/{x *x*(x+2)} = 1
now remove common x from numerator and denominator and multiply denominator to RHS so we get
x + 2+x +1 = x*x + 2x
Solve this equation and you get
x *x = 3
so you get two values of x
Intern  B
Joined: 10 Jul 2018
Posts: 6
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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The number of roots is +/- ✓3 i.e 2 roots

Posted from my mobile device
Manager  G
Joined: 21 Feb 2019
Posts: 125
Location: Italy
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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

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

Existence conditions: $$x =$$ R - {0, -1, -2}.

$$2x + 3 = x^2 + 2x$$

$$x = {-\sqrt{3}, + \sqrt{3}}$$.

Hence, C.
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MEMENTO AUDERE SEMPER How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None   [#permalink] 30 Mar 2019, 12:08
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