Useful property #1: (a + b)/c = a/c + b/c
For example, (2 + 5)/11 = 2/11 + 5/11

Useful property #2: 1/(a/b) = b/a
For example, 1/(3/5) = 5/3

By Property #1 we can rewrite both Quantities as follows:
QUANTITY A: \(\frac{x^2 + 1}{x}=\frac{x^2}{x} + \frac{1}{x}\)\(=x + \frac{1}{x}\)

QUANTITY B: \(\frac{y^2 + 1}{y}=\frac{y^2}{y} + \frac{1}{y}\)\(=y + \frac{1}{y}\)

Since \(x=\frac{1}{y}\), we can take Quantity A, and replace x with 1/y to get:
QUANTITY A: \(\frac{1}{y} + \frac{1}{{1/y}}\)
QUANTITY B: \(y + \frac{1}{y}\)


Use Property #2 to rewrite Quantity A as follows:
QUANTITY A: \(\frac{1}{y} + y\)
QUANTITY B: \(y + \frac{1}{y}\)

Answer: C

Cheers,
Brent