Carcass wrote:
\(\frac{1-x}{x-1}=\frac{1}{x}\)
Quantity A |
Quantity B |
x |
\(\frac{-1}{2}\) |
Aside: from the given equation, we know that x ≠ 0 and we know that x-1 ≠ 0
Here's why:
If x = 0, we get: (1-0)/(0-1) = 1/0
Simplify to get: -1 = 1/0 DOESN'T WORK
So, x ≠ 0
Likewise,
if x-1 = 0, then x = 1
If we plug in 1 for x, we get: (1-1)/(1-1) = 1/1
Simplify to get: 0/0 = 1/1 DOESN'T WORK
So, x-1 ≠ 0
--------------------------------
Okay, now for a different approach....
Notice that 1-x = -1(-1 + x) =
-1(x-1)So, let's take (1-x)/(x-1) = 1/x and replace (1-x) with
-1(x-1)We get:
-1(x-1)/(x-1) = 1/x
Simplify to get: -1 = 1/x
Solve to get: x = -1
So, we have:
Quantity A: -1
Quantity B: -1/2
Answer: B
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Brent Hanneson – Creator of greenlighttestprep.com
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