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

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Joined: 30 May 2018
Posts: 89
GMAT 1: 620 Q42 V34
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How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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New post 21 Mar 2019, 12:11
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

35% (02:09) correct 65% (02:28) wrong based on 46 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
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Posts: 147
Location: Bangladesh
GMAT 1: 490 Q44 V15
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How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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New post Updated on: 29 Mar 2019, 18:38
X can be √3 or -√3
X cannot be 0, -1 or -2

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

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New post 21 Mar 2019, 14:57
I would go for C.
If any other short formula is available, pls share.

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

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New post 29 Mar 2019, 13:17
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.
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Re: How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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New post 29 Mar 2019, 18:41
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.
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Re: How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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New post 30 Mar 2019, 00:22
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
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How many solutions does 1/[x*(x+1)]+1/[x*(x+2)]=1/(x+1) have? A. None  [#permalink]

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New post 30 Mar 2019, 00:32
The number of roots is +/- ✓3 i.e 2 roots

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

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New post 30 Mar 2019, 12:08
\(\frac{1}{x{(x+1)}} + \frac{1}{x{(x+2)}} = \frac{1}{(x+1)}\)

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


Existence conditions: \(x =\) R - {0, -1, -2}.

\(2x + 3 = x^2 + 2x\)

\(x = {-\sqrt{3}, + \sqrt{3}}\).

Hence, C.
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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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