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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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If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? [#permalink]

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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.
[Reveal] Spoiler: OA

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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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New post 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
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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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New post 22 Aug 2016, 19:50
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]

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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]

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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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Re: If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?   [#permalink] 17 Sep 2017, 08:24
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