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