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Which of the following is equal to

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Math Revolution GMAT Instructor
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Which of the following is equal to [#permalink]

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New post 12 Apr 2018, 02:00
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A
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C
D
E

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  15% (low)

Question Stats:

84% (01:08) correct 16% (01:18) wrong based on 56 sessions

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[GMAT math practice question]

Which of the following is equal to \(\frac{x!}{(x+1)!} + \frac{(x+1)!}{(x+2)!}\)?

\(A. 1+\frac{1}{x}\)
\(B. 1+\frac{1}{(x+1)}\)
\(C. \frac{(2x+3)}{(x+1)(x+2)}\)
\(D. \frac{1}{x(x+1)}\)
\(E. \frac{(2x-1)}{{(x+1)(x+2)}}\)

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Re: Which of the following is equal to [#permalink]

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New post 12 Apr 2018, 02:11
1
x!/(x+1)! +(x+1)!/(x+2)!

= x!/(x+1)x! +(x+1)!/(x+2)(x+1)!

=1/(x+1) + 1/(x+2)

= {(x+2)+(x+1)}/(x+1)(x+2)

= (2x+3)/ (x+1)(x+2)



Answer = C



Important formula used : n! = n(n-1)!

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Math Revolution GMAT Instructor
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Re: Which of the following is equal to [#permalink]

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New post 15 Apr 2018, 18:45
=>
x! / ( x + 1 )! + ( x + 1 )! / ( x + 2 )!
= x! / {x! * (x+1)} + (x+1)! / { (x+1)! * (x+2) }
= 1/(x+1) + 1/(x+2) = (2x+3)/(x+1)(x+2)

Therefore, C is the answer.
Answer: C
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Re: Which of the following is equal to [#permalink]

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New post 26 Apr 2018, 07:29
MathRevolution wrote:
=>
x! / ( x + 1 )! + ( x + 1 )! / ( x + 2 )!
= x! / {x! * (x+1)} + (x+1)! / { (x+1)! * (x+2) }
= 1/(x+1) + 1/(x+2) = (2x+3)/(x+1)(x+2)

Therefore, C is the answer.
Answer: C


HI, how did you get this?
x! / {x! * (x+1)}
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Re: Which of the following is equal to [#permalink]

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New post 26 Apr 2018, 07:44
MathRevolution wrote:
[GMAT math practice question]

Which of the following is equal to \(\frac{x!}{(x+1)!} + \frac{(x+1)!}{(x+2)!}\)?

\(A. 1+\frac{1}{x}\)
\(B. 1+\frac{1}{(x+1)}\)
\(C. \frac{(2x+3)}{(x+1)(x+2)}\)
\(D. \frac{1}{x(x+1)}\)
\(E. \frac{(2x-1)}{{(x+1)(x+2)}}\)


Ans: C

to avoide the lengthy calculaton we can put x=2 . this way it becomes easier to get the ans.
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Re: Which of the following is equal to [#permalink]

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New post 26 Apr 2018, 07:46
1
antarcticsugar wrote:
MathRevolution wrote:
=>
x! / ( x + 1 )! + ( x + 1 )! / ( x + 2 )!
= x! / {x! * (x+1)} + (x+1)! / { (x+1)! * (x+2) }
= 1/(x+1) + 1/(x+2) = (2x+3)/(x+1)(x+2)

Therefore, C is the answer.
Answer: C


HI, how did you get this?
x! / {x! * (x+1)}


Well x! means= x*(x-1)*(x-2)*.....(x-x)

Well treat it like this when you write 4! what does it means??
It means 4x3x2x1 and we know that 3! = 3x2x1
so 4! = 4* 3!

Hope it is clear..
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Re: Which of the following is equal to   [#permalink] 26 Apr 2018, 07:46
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