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A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

Now we can say that \(x < x+1\). So rewriting \(\frac{x}{x+1} < 1\) . Hence Quantity A is always less than 1.

Now we can say that \(x > x-1\). So rewriting \(\frac{x}{x-1} > 1\) . Multiplying -1 to the numerator or denominator \(\frac{-x}{1-x} > 1\). Hence Quantity B is always greater than 1.

So combining these two Quantity A < 1 < Quantity B. Hence option B is correct. _________________

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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

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A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

We can rewrite (-x)/(1-x) in a "nicer" way. Given: (-x)/(1-x) Factor -1 from top and bottom to get: (-1)(x)/(-1)(-1 + x) Rewrite part in red as follows: (-1)(x)/(-1)(x - 1) The -1's cancel out to get: x/(x - 1) In other words, (-x)/(1-x) = x/(x - 1)

We have: Quantity A: x/ x + 1) Quantity B: x/(x - 1)

Since x > 1, we know that x is POSITIVE So, we can safely divide both quantities by x to get: Quantity A: 1/(x + 1) Quantity B: 1/(x - 1)

Also, since x > 1, we know that (x - 1) is POSITIVE So, we can safely multiply both quantities by (x - 1) to get: Quantity A: (x - 1)/(x + 1) Quantity B: 1

At this point, we might already see that 1 must be greater than (x - 1)/(x + 1) However, let's keep going with our strategy....

Since x > 1, we know that (x + 1) is POSITIVE So, we can safely multiply both quantities by (x + 1) to get: Quantity A: (x - 1) Quantity B: (x + 1)

Subtract x from both quantities to get: Quantity A: -1 Quantity B: 1

Answer: B

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In such questions, plugin is not a good strategy. Always simplify it first as much as you can, then go to see which Quantity is greater. Here's how you should do:

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

We can write Quantity B as: x/(x-1)

As we know x is positive and greater than 1, so we can cancel out x on both sides of the Quantity. (Remember that Quantitative comparison has rule similar to inequality, so if we divide both sides by any positive number, inequality will not change;.

Thus, we'll get

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

Now, multiplying both sides by (x+1)(x-1), we'll get

Quantity A: (x-1) Quantity B: (x+1)

Thus, Quantity B > Quantity A

So, Choice B is Correct.
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correct: B x is a positive integer, so x+1 is more than x, and x divided by x+1 is something less than 1 we can write -x/ 1-x as x / x-1 by multiplying both the numerator and the denominator by -1. As x is a positive integer, x-1 is less than x and x divided by a thing less than x is something more than 1. So B is bigger than A. _________________

X/X+1 ? -X/1-X As we know x>1 So, B both A nd B will always be +ve Re write B as X/X-1 now both the numerators are equal. W just have to compare denominator now As X-1< X+1(We know that X>1, so X can not be negative or 1) Hence B > A