Carcass wrote:
\(\frac{2}{d}= \frac{2-d}{d-2}\)
Quantity A |
Quantity B |
d |
0 |
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.
Great question!!!!!
Given: \(\frac{2}{d}= \frac{2-d}{d-2}\)
Cross multiply to get: 2(d - 2) = d(2 - d)
Expand: 2d - 4 = 2d - d²
Subtract 2d from both sides to get: -4 = -d²
Multiply both sides by -1 to get: 4 = d²
So, either d = 2 or d = -2
It SEEMS that we have two solutions, but this is not the case
If we plug d = -2 into the given equation,\(\frac{2}{d}= \frac{2-d}{d-2}\), we get: \(\frac{2}{-2} = \frac{4}{-4}\)
Since this equation checks out, we can conclude that d = -2 is a valid solution
HOWEVER, if we plug d = 2 into the given equation,\(\frac{2}{d}= \frac{2-d}{d-2}\), we get: \(\frac{2}{2} = \frac{0}{0}\)
Since this equation does NOT check out, we can see that d = 2 is NOT a valid solution
Since there's only one possible value of d (d = -2)
So, we get:
Quantity A: -2
Quantity B: 0
Answer: B
Cheers,
Brent