GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Feb 2020, 23:40 ### 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

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.  # How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None

Author Message
TAGS:

### Hide Tags

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]

### Show Tags

2 00:00

Difficulty:   75% (hard)

Question Stats: 51% (02:01) correct 49% (02:31) wrong based on 75 sessions

### HideShow timer Statistics

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
Current Student G
Joined: 11 Feb 2013
Posts: 274
Location: United States (TX)
Schools: Neeley '21 (A$) GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38 GPA: 3.05 WE: Analyst (Commercial Banking) How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None [#permalink] ### Show Tags X can be √3 or -√3 X cannot be 0, -1 or -2 Posted from my mobile device Originally posted by BelalHossain046 on 21 Mar 2019, 13:56. Last edited by BelalHossain046 on 29 Mar 2019, 17:38, edited 1 time in total. Current Student G Joined: 11 Feb 2013 Posts: 274 Location: United States (TX) Schools: Neeley '21 (A$)
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]

### Show Tags

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: 952
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

### Show Tags

1
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
Current Student G
Joined: 11 Feb 2013
Posts: 274
Location: United States (TX)
Schools: Neeley '21 (A\$)
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]

### Show Tags

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]

### Show Tags

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: 09 Jul 2018
Posts: 6
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

### Show Tags

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

Posted from my mobile device
Manager  G
Joined: 21 Feb 2019
Posts: 124
Location: Italy
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

### Show Tags

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

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

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

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

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

Hence, C.
VP  P
Joined: 24 Nov 2016
Posts: 1207
Location: United States
How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

### Show Tags

MBA20 wrote:
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

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

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

$$2x+3 = \frac{x(x + 2)(x + 1)}{(x + 1)}$$

$$2x+3 = x(x + 2)…2x+3=x^2+2x…x^2-3=0…x^2=3…x=(√3,-√3)$$

Ans (C)
SVP  D
Joined: 03 Jun 2019
Posts: 2004
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

### Show Tags

MBA20 wrote:
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

[(x+2)+(x+1)]/[x(x+1)(x+2)]= 1/(x+1)
2x+3 = x(x+2)
x^2=3
x=+-sqrt(3)

IMO C

Posted from my mobile device Re: How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None   [#permalink] 11 Dec 2019, 09:20
Display posts from previous: Sort by

# How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  