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y=x+1/x -1, what is 1/y ?
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27 Jan 2020, 04:00
27 Jan 2020, 04:00
Expert Reply
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Question Stats:
72% (00:42) correct
27% (00:52) wrong based on 40 sessions
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If \(x \neq 0\) and \(y=\frac{x+1}{x} -1\), what is \(\frac{1}{y}\) ?
A. \(x\)
B. \(\frac{1}{x
}\)
C. \(-x+1\)
D. \(\frac{x+1}{x-1}\)
E. \(-(x+1)\)
Kudos for the right answer and explanation
A. \(x\)
B. \(\frac{1}{x
}\)
C. \(-x+1\)
D. \(\frac{x+1}{x-1}\)
E. \(-(x+1)\)
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: y=x+1/x -1, what is 1/y ?
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27 Jan 2020, 09:51
27 Jan 2020, 09:51
1
Carcass wrote:
If \(x \neq 0\) and \(y=\frac{x+1}{x} -1\), what is \(\frac{1}{y}\) ?
A. \(x\)
B. \(\frac{1}{x
}\)
C. \(-x+1\)
D. \(\frac{x+1}{x-1}\)
E. \(-(x+1)\)
Kudos for the right answer and explanation
A. \(x\)
B. \(\frac{1}{x
}\)
C. \(-x+1\)
D. \(\frac{x+1}{x-1}\)
E. \(-(x+1)\)
Kudos for the right answer and explanation
Key concept: If \(y = \frac{a}{b}\), then \(\frac{1}{y} = \frac{b}{a}\)
Take: \(y=\frac{x+1}{x} -1\)
Rewrite \(1\) as \(\frac{x}{x}\) to get: \(y=\frac{x+1}{x} -\frac{x}{x}\)
Combined numerators to get: \(y=\frac{(x+1) - x}{x}\)
Simplify to get: \(y=\frac{1}{x}\)
Apply key concept to get: \(\frac{1}{y}=\frac{x}{1}\)
Simplify: \(\frac{1}{y}=x\)
Answer: A
Cheers,
Brent
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Given Kudos: 0
GPA: 3.72
Re: y=x+1/x -1, what is 1/y ?
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28 Jan 2020, 05:45
28 Jan 2020, 05:45
1
Carcass wrote:
If \(x \neq 0\) and \(y=\frac{x+1}{x} -1\), what is \(\frac{1}{y}\) ?
A. \(x\)
B. \(\frac{1}{x
}\)
C. \(-x+1\)
D. \(\frac{x+1}{x-1}\)
E. \(-(x+1)\)
Kudos for the right answer and explanation
A. \(x\)
B. \(\frac{1}{x
}\)
C. \(-x+1\)
D. \(\frac{x+1}{x-1}\)
E. \(-(x+1)\)
Kudos for the right answer and explanation
We have: \(y=\frac{x+1}{x} -1\)
\(=> y=1 + \frac{1}{x} -1\)
\(=> y=\frac{1}{x}\)
Taking reciprocal on both sides:
\(\frac{1}{y} = x\)
Answer A
