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# Which of the following equals the reciprocal of x - 1/y, where x - 1/y

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Math Expert
Joined: 02 Sep 2009
Posts: 51067
Which of the following equals the reciprocal of x - 1/y, where x - 1/y  [#permalink]

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27 Jun 2018, 20:41
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Difficulty:

15% (low)

Question Stats:

72% (00:40) correct 28% (01:07) wrong based on 71 sessions

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Which of the following equals the reciprocal of $$x - \frac{1}{y}$$, where $$x - \frac{1}{y}$$ different from zero ?

(A) $$\frac{1}{x} - y$$

(B) $$\frac{-y}{x}$$

(C) $$\frac{y}{x - 1}$$

(D) $$\frac{x}{xy - 1}$$

(E) $$\frac{y}{xy - 1}$$

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Posts: 2269
Re: Which of the following equals the reciprocal of x - 1/y, where x - 1/y  [#permalink]

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27 Jun 2018, 21:39
2
1

Solution

To find:
• What is the value of the reciprocal of $$x – \frac{1}{y}$$, if $$x – \frac{1}{y}$$ is not equal to 0

Approach and Working:
We can simplify the given expression first in the following manner:
• $$x – \frac{1}{y}$$ = $$\frac{xy – 1}{y}$$

Therefore, the reciprocal = $$\frac{y}{xy – 1}$$

Hence, the correct answer is option E.

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Which of the following equals the reciprocal of x - 1/y, where x - 1/y  [#permalink]

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28 Jun 2018, 18:41
Bunuel wrote:
Which of the following equals the reciprocal of $$x - \frac{1}{y}$$, where $$x - \frac{1}{y}$$ different from zero ?

(A) $$\frac{1}{x} - y$$

(B) $$\frac{-y}{x}$$

(C) $$\frac{y}{x - 1}$$

(D) $$\frac{x}{xy - 1}$$

(E) $$\frac{y}{xy - 1}$$

To take the reciprocal of a rational expression with fractions, first simplify the expression to get a consolidated fraction, then flip the fraction over.

(1) Simplify $$x -\frac{1}{y}$$

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

$$((\frac{y}{y}*\frac{x}{1})-\frac{1}{y})=$$

$$(\frac{xy}{y}-\frac{1}{y})=\frac{xy-1}{y}$$

(2) Invert the fraction $$\frac{xy-1}{y}$$

$$\frac{y}{xy - 1}$$

* To find the reciprocal of a real number, divide 1 by the number. Thus the reciprocal of $$\frac{xy-1}{y}$$ is
$$\frac{1}{(\frac{xy-1}{y})}$$. As with any division by a fraction, invert the divisor fraction and multiply:
$$\frac{1}{(\frac{xy-1}{y})}=(1*\frac{y}{xy-1})=\frac{y}{xy-1}$$
Instead of going through that process to find the reciprocal of a factional expression, once the expression is simplified, just invert the fraction.
Which of the following equals the reciprocal of x - 1/y, where x - 1/y &nbs [#permalink] 28 Jun 2018, 18:41
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