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If \(xy ≠ 0\) and \(\frac{1}{x} - \frac{1}{y} =cx\), which of the following is equal to c ?
A. \(\frac{x}{y(1 - x^2)}\)
B. \(\frac{1}{-x^2y}\)
C. \(\frac{y - x}{x^2y}\)
D. \(\frac{y - x}{y}\)
E. \(\frac{y}{y - x}\)
PS21148
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A. \(\frac{x}{y(1 - x^2)}\)
B. \(\frac{1}{-x^2y}\)
C. \(\frac{y - x}{x^2y}\)
D. \(\frac{y - x}{y}\)
E. \(\frac{y}{y - x}\)
PS21148
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Bunuel
Given: \(\frac{1}{x} - \frac{1}{y} =cx\)
Multiply both sides \(\frac{1}{x}\) by to get: \((\frac{1}{x})(\frac{1}{x} - \frac{1}{y}) = (\frac{1}{x})(cx)\)
Expand and simplify to get: to get: \(\frac{1}{x^2} - \frac{1}{xy} = c\)
Check the answer choices... not there!
Looks like we need to rewrite the left side as one entire fraction
Rewrite with common denominators to get: \(\frac{y}{x^2y} - \frac{x}{x^2y} = c\)
Combine: \(\frac{y - x}{x^2y} = c\)
Answer: C
Cheers,
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General Discussion
yashikaaggarwal
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Joined: 18 Jan 2020
Last visit: 10 Aug 2026
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Schools: Cranfield (A) Warwick MiM "23 (M)
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=> (1/x)-(1/y)=CX
=> (Y-X)/xy=CX
=> (Y-X)/x^2y = C
Answer is C
Posted from my mobile device
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=> (Y-X)/xy=CX
=> (Y-X)/x^2y = C
Answer is C
Posted from my mobile device
_________________
Bunuel
\(\frac{1}{x} - \frac{1}{y} =cx\)
i.e. \(\frac{y-x}{xy} =cx\)
i.e. \(\frac{y-x}{x^2y} =c\)
Answer: Option C
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