Carcass wrote:
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. \(\frac{y}{y - x}\)
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,
Brent