Carcass wrote:
If x and y are integers and \(\frac{(x^2-y^2)}{xy}=2\), what is \(\frac{x}{y}-\frac{y}{x}\)?
(A) 1/2
(B) 2
(C) 6
(D) 8
(E) 12
Great question!!!
Since our goal is to find the value of \(\frac{x}{y}-\frac{y}{x}\), and since we are given an equation with an entire fraction, let's first rewrite \(\frac{x}{y}-\frac{y}{x}\) as an entire fraction and see where that leads us.
Take: \(\frac{x}{y}-\frac{y}{x}\)
Rewrite both fractions with the same common denominator: \(\frac{x^2}{xy}-\frac{y^2}{xy}\)
Combine the numerators to get: : \(\frac{x^2 - y^2}{xy}\)
Since it's given that \(\frac{(x^2-y^2)}{xy}=2\), we can conclude the following: \(\frac{x}{y}-\frac{y}{x}=\frac{x^2 - y^2}{xy}=2\)
Answer: B