Carcass wrote:
\(X > 1\)
Quantity A |
Quantity B |
\(\frac{x}{(x+1)}\) |
\(\frac{-x}{1-x}\) |
Quantity A: x/(x+1)
Quantity B: -x/(1-x)
First recognize that we can rewrite quantity B by factoring out a -1 from the numerator and denominator.
That is: -x = (-1)(x) and 1-x = -1(-1 + x) = -1(x - 1)
So, -x/(1-x) = (-1)(x)/(-1)(x - 1) = x/(x - 1)
So we get:
Quantity A: x/(x + 1)
Quantity B: x/(x - 1)
Now let's find a common denominator.
To do so, we'll take Quantity A and multiply numerator and denominator by (x - 1)
And we'll take Quantity B and multiply numerator and denominator by (x + 1)
When we do this, we get:
Quantity A: (x² - x)/(x² - 1)
Quantity B: (x² + x)/(x² - 1)
Next, since x > 1, we know that x² > 1, which means x² - 1 is POSITIVE
As such, we can multiply both quantities by x² - 1 to get:
Quantity A: x² - x
Quantity B: x² + x
Now it's pretty easy from here. Subtract x² from both quantities to get:
Quantity A: -x
Quantity B: x
Add x to both quantities to get:
Quantity A: 0
Quantity B: 2x
Since x is POSITIVE, 2x must be POSITIVE, which means the correct answer is B
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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