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# Which of the following is equivalent to [1 - {1/(x + 1)]/x for all

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Joined: 02 Sep 2009
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Which of the following is equivalent to [1 - {1/(x + 1)]/x for all [#permalink]

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15 Jan 2018, 05:12
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Which of the following is equivalent to $$\frac{1 - \frac{1}{x + 1}}{x}$$ for all values of x for which both expressions are defined?

(A) 1
(B) x + 1
(C) 1/x
(D) 1/(x + 1)
(E) x^2 + x
[Reveal] Spoiler: OA

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Which of the following is equivalent to [1 - {1/(x + 1)]/x for all [#permalink]

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15 Jan 2018, 06:52
Bunuel wrote:
Which of the following is equivalent to $$\frac{1 - \frac{1}{x + 1}}{x}$$ for all values of x for which both expressions are defined?

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

Method 1: Algebraic

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

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

Option D

-----------------------------

Method 2: Chose smart number for $$x$$. let $$x=1$$

therefore $$\frac{1 - \frac{1}{x + 1}}{x}=1-\frac{1}{2}=\frac{1}{2}$$

Substitute $$x=1$$ in options and only option D$$=\frac{1}{2}$$
Which of the following is equivalent to [1 - {1/(x + 1)]/x for all   [#permalink] 15 Jan 2018, 06:52
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# Which of the following is equivalent to [1 - {1/(x + 1)]/x for all

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