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If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y?

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Russ19
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If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y? [#permalink] New post   Updated on: 14 Feb 2020, 00:08
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If \(y = \frac{x^{-1} – 1}{ x^{-1} + 1}\), what is x in terms of y?


(A) \(\frac{y – 1}{y + 1}\)

(B) \(\frac{y + 1}{y – 1}\)

(C) \(\frac{1- y}{1 + y}\)

(D) \(\frac{1+ y}{1 - y}\)

(E) \(\frac{y}{y + 1}\)

Source: GMAT Quantum
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C

Originally posted by Russ19 on 13 Feb 2020, 19:28.
Last edited by Bunuel on 14 Feb 2020, 00:08, edited 1 time in total.
Renamed the topic and edited the question.
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If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y? [#permalink] New post   13 Feb 2020, 21:31
Expert Reply
sjuniv32 wrote:
If y = \(\frac{x^{-1} – 1}{ x^{-1} + 1}\), what is x in terms of y?

(A) \(\frac{y – 1}{y + 1}\\
\)

(B) \(\frac{y + 1}{y – 1}\)

(C) \(\frac{1- y}{1 + y}\\
\)

(D) \(\frac{1+ y}{1 - y}\)

(E) \(\frac{y}{y + 1}\)

Source: GMAT Quantum


Two ways..

1) simplify..
y = \(\frac{x^{-1} – 1}{ x^{-1} + 1}=\frac{\frac{1}{x}-1}{\frac{1}{x}+1}=\frac{\frac{1-x}{x}}{\frac{x+1}{x}}=\frac{1-x}{x+1}\)...
So \(y(x+1)=1-x.....yx+y=1-x....yx+x=1-y....x=\frac{1-y}{1+y}\)

2) Take a value for x...
Let x=1/2
y = \(\frac{x^{-1} – 1}{ x^{-1} + 1}=\frac{\frac{1}{2}^{-1}-1}{\frac{1}{2}^{-1}+1}=\frac{2-1}{2+1}=\frac{1}{3}\)

Check each for 1/2 when you put y as 1/3.
Wherever you have y-1 or 1/3 - 1, the answer will be negative, so discard those options as we are looking for positive 1/2.
C. \(\frac{1- y}{1 + y}=\frac{1-\frac{1}{3}}{1+\frac{1}{3}}=\frac{\frac{2}{3}}{\frac{4}{3}}=\frac{2}{4}=\frac{1}{2}\)


C
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Re: If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y? [#permalink] New post   13 Feb 2020, 22:30
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Expert Reply
sjuniv32 wrote:
If y = \(\frac{x^{-1} – 1}{ x^{-1} + 1}\), what is x in terms of y?

(A) \(\frac{y – 1}{y + 1}\\
\)

(B) \(\frac{y + 1}{y – 1}\)

(C) \(\frac{1- y}{1 + y}\\
\)

(D) \(\frac{1+ y}{1 - y}\)

(E) \(\frac{y}{y + 1}\)

Source: GMAT Quantum


Solution


• \(y = \frac{(x^{-1} – 1)}{ (x^{-1} +1)}\)
    \(⟹ y = ({\frac{1}{x} - 1})/({\frac{1}{x}+1})\)
    \(⟹ y = \frac{(1 – x)}{(1+x)} \)
    \(⟹ y(1+x) = (1 – x) \)
    \(⟹ y+ yx= 1 – x \)
    \(⟹ x(1 +y) = (1-y) \)
    \(⟹ x= \frac{(1-y)}{ (1+y)} \)
Thus, the correct answer is Option C
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Re: If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y? [#permalink] New post   21 Dec 2020, 09:00
How did you go from y+yx=1–x to x(1+y)=(1−y)

Everything makes good sense till there.
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Re: If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y? [#permalink]
21 Dec 2020, 09:00
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