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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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MathRevolution
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If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? [#permalink] New post   21 Aug 2016, 00:04
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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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B
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chetan2u
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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] New post   21 Aug 2016, 00:46
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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] New post   22 Aug 2016, 19:50
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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] New post   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 ?
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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] New post   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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If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? [#permalink] New post   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

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] New post   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....
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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] New post   28 Oct 2018, 07:02
Eladt wrote:
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.
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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]
28 Oct 2018, 07:02
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