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Which of the following is equal to

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Which of the following is equal to [#permalink]

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[GMAT math practice question]

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

\(A. 1+\frac{1}{x}\)
\(B. 1+\frac{1}{(x+1)}\)
\(C. \frac{(2x+3)}{(x+1)(x+2)}\)
\(D. \frac{1}{x(x+1)}\)
\(E. \frac{(2x-1)}{{(x+1)(x+2)}}\)
[Reveal] Spoiler: OA

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

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New post 12 Apr 2018, 02:11
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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Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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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] 15 Apr 2018, 18:45
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