Explanation

Another approach is to use Matching Operations

Given:
Quantity A: 1/x
Quantity B: (1 + x)

Since x ≠ 0, we can be certain that x² is POSITIVE
So, we can safely multiply both quantities by x² to get:
Quantity A: x²/x
Quantity B: (1 + x)

Simplify to get:
Quantity A: x
Quantity B: 1 + x

Subtract x from both sides to get:
Quantity A: 0
Quantity B: 1

Answer: B

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As x > 0, no matter what 1/x^2 + 1/x will always be great than 1/x, Hence B

Quantity A Quantity B
1/X (1+X)/X^2
Multiply both by X
1 (1+X)/X
1 1/X + X/X
1 1/X + 1
Since X Always >0 , Then Quantity B is always greater.
Answer is B.

Another approach

Given:
Quantity A: 1/x
Quantity B: (1 + x)/x²

USEFUL FRACTION PROPERTY: (a + b)/c = a/b + a/c

So, we can rewrite Quantity B as follows:
Quantity A: 1/x
Quantity B: 1/x² + x/x²

Simplify Quantity B:
Quantity A: 1/x
Quantity B: 1/x² + 1/x

Subtract 1/x from both quantities to get:
Quantity A: 0
Quantity B: 1/x²

Since x > 0, we know that x² > 0, which means 1/x² > 0

Answer: B
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If we're not sure how to proceed, we can always test some values to at least eliminate some answer choices.

We're told that x > 0

So, let's first test x = 1
We get:
QUANTITY A: 1/1 = 1
QUANTITY B: (1 + 1)/1² = 2/1 = B
In this case, Quantity B is greater
This means we can ELIMINATE A and C. So, if we must guess, we're down to a 50-50 proposition!

Let's test some more values.


Test x = 0.1
QUANTITY A: 1/0.1 = 10
QUANTITY B: (1 + 0.1)/0.1² = 1.1/0.01 = 110
In this case, Quantity B is greater


Test x = 3
QUANTITY A: 1/3 = 1/3
QUANTITY B: (1 + 3)/3² = 4/9
In this case, Quantity B is greater


Test x = 10
QUANTITY A: 1/3 = 1/10
QUANTITY B: (1 + 10)/10² = 11/100
In this case, Quantity B is greater

At this point, it SEEMS like Quantity B will always be greater?
Can we be 100% sure that the answer B?
No, but B would be a reasonable guess, and guess what? The correct answer IS B.

Cheers,
Brent


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