APPROACH #1: Number sense.
Since x is positive, we know that x+1 must also be positive.
So, both quantities represent positive fractions.
Since x < x+1, we know that the fraction x/(x+1) must be less than 1
Conversely, since x < x+1, we know that the fraction (x+1)/1 must be greater than 1

So we have:
QUANTITY A: Some positive fraction that's less than 1
QUANTITY B: Some positive fraction that's greater than 1

Answer: B



APPROACH #2: Matching operations (see video below for more on this strategy)
Given:
Quantity A: \( \frac{x}{x+1}\)
Quantity B: \(\frac{x+1}{x} \)

Since we're told x is positive, we can safely multiply both quantities by x to get:
Quantity A: \( \frac{x^2}{x+1}\)
Quantity B: \(x+1 \)

Since x is positive, we know that x+1 is positive, which means we can safely multiply both quantities by x+1 to get:
Quantity A: \( x^2\)
Quantity B: \((x+1)^2\)

Expand and simplify Quantity B:
Quantity A: \( x^2\)
Quantity B: \(x^2 + 2x + 1\)

Subtract x² from both quantities:
Quantity A: \(0\)
Quantity B: \(2x + 1\)

Since x is positive, we know that 2x must be positive, which means 2x+1 must be positive, which means Quantity B is definitely greater than 0

Answer: B

RELATED VIDEO