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Useful property: \(\frac{a-b}{b-a} = -1\)

Here's why: we can take \(b - a\) and factor out \(-1\) to get: \(b - a = (-1)(-b + a)\)

Since \(-b + a = a - b\), we get: \(b - a = (-1)(-b + a)= (-1)(a -b)\)

So,\(\frac{a-b}{b-a} = \frac{a-b}{-1(a-b)}= -1\)

So our two quantities and now look like this:
QUANTITY A: \(\frac{c-1}{c+1}\)

QUANTITY B: \(-1\)

Since \(0<c<1\), we can be certain that \(c+1\) is POSITIVE
So, we can safely multiply both quantities by \(c+1\) to get:
QUANTITY A: \(c-1\)
QUANTITY B: \(-1(c+1)\)

Expand to get:
QUANTITY A: \(c-1\)
QUANTITY B: \(-c-1\)

Add \(1\) to both quantities:
QUANTITY A: \(c\)
QUANTITY B: \(-c\)

Add \(c\) to both quantities:
QUANTITY A: \(2c\)
QUANTITY B: \(0\)

Since we are told that \(c\) is positive, Quantity A must be greater

Answer: A
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here quant B is -1
for quant A
let c=0.1
quant A=(0.1-1)/(1+0.1)=-0.8181...
quant A>quant B

let c=0.9
quant A=(0.9-1)/(1+0.9)=-0.0526...
quant A>quant B

option A is correct
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