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# For all values of x where x > 2, which of the following is equivalent

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Math Expert
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For all values of x where x > 2, which of the following is equivalent  [#permalink]

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23 Nov 2016, 05:51
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Difficulty:

5% (low)

Question Stats:

92% (01:28) correct 8% (02:32) wrong based on 80 sessions

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For all values of x where x > 2, which of the following is equivalent to $$\frac{x!+(x−1)!}{(x+2)!}$$?

A. 1/(x^2+2)
B. 1/(x^2+2x)
C. 1/(x+2)
D. 1/(x^2)
E. 1/(x+1)!

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Re: For all values of x where x > 2, which of the following is equivalent  [#permalink]

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23 Nov 2016, 05:59
Bunuel wrote:
For all values of x where x > 2, which of the following is equivalent to $$\frac{x!+(x−1)!}{(x+2)!}$$?

A. 1/(x^2+2)
B. 1/(x^2+2x)
C. 1/(x+2)
D. 1/(x^2)
E. 1/(x+1)!

IMO B
$$\frac{x!+(x−1)!}{(x+2)!}$$can be simplified as $$\frac{x* (x-1)! + (x-1)!}{(x+2)(x+1)x(x-1)!}$$
cancelling common terms we are left with $$\frac{1}{x(x+2)}$$
which is B
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Re: For all values of x where x > 2, which of the following is equivalent  [#permalink]

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23 Nov 2016, 06:58
I say choice (B).

I plugged x=3 into the answer choices and x!+(x−1)!/(x+2)! simplified to 1/15.

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Re: For all values of x where x > 2, which of the following is equivalent  [#permalink]

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23 Nov 2016, 08:17
Bunuel wrote:
For all values of x where x > 2, which of the following is equivalent to $$\frac{x!+(x−1)!}{(x+2)!}$$?

A. 1/(x^2+2)
B. 1/(x^2+2x)
C. 1/(x+2)
D. 1/(x^2)
E. 1/(x+1)!

= $$\frac{x!+(x−1)!}{(x+2)!}$$

= $$\frac{x( x - 1) !+(x−1)!}{(x+2)( x + 1) x ( x - 1)!}$$

= $$\frac{( x - 1) ! ( x + 1)}{(x+2)( x + 1) x ( x - 1)!}$$

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

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

PS : I will ordinarily employ gracie90 's plug in approach for solving this question quickly
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Re: For all values of x where x > 2, which of the following is equivalent  [#permalink]

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08 Oct 2018, 12:32
Bunuel wrote:
For all values of x where x > 2, which of the following is equivalent to $$\frac{x!+(x−1)!}{(x+2)!}$$?

A. 1/(x^2+2)
B. 1/(x^2+2x)
C. 1/(x+2)
D. 1/(x^2)
E. 1/(x+1)!

when we have variables in question stem and in answer choices , it's better to assign values for the variables.

let x be 3

$$\frac{x!+(x−1)!}{(x+2)!}$$

= 3! + 2! / 5!

= 8 / 120

= 1 /15

Put x=3 in option B . the result is same.

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Re: For all values of x where x > 2, which of the following is equivalent  [#permalink]

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10 Oct 2018, 17:45
Bunuel wrote:
For all values of x where x > 2, which of the following is equivalent to $$\frac{x!+(x−1)!}{(x+2)!}$$?

A. 1/(x^2+2)
B. 1/(x^2+2x)
C. 1/(x+2)
D. 1/(x^2)
E. 1/(x+1)!

[x! + (x - 1)!]/(x + 2)!

In the numerator, we factor out the common (x - 1)! from both terms. We also expand the factorial in the denominator, obtaining:

[(x - 1)!(x + 1)]/[(x + 2)(x + 1)(x)(x - 1)!]

1/[(x + 2)(x)]

1/(x^2 + 2x)

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Re: For all values of x where x > 2, which of the following is equivalent   [#permalink] 10 Oct 2018, 17:45
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