If a = \(\frac{2x}{1 - x}\) and b = \(\frac{1 + x}{1 - x}\), then a2 - b2 in the simplest form is
A
\(\frac{3x + 1}{x - 1}\)
B
\(\frac{3x^2 - 1}{(x - 1)}\)2
C
x\(\frac{3x - 2}{1 - x}\)
D
\(\frac{3x^2 - 1}{(x - 1)}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
a2 - b2 = (\(\frac{2x}{1 - x}\))2 - (\(\frac{1 + x}{1 - x}\))2
= (\(\frac{2x}{1 - x} + \frac{1 + x}{1 - x}\))(\(\frac{2x}{1 - x} - \frac{1 + x}{1 - X}\))
= (\(\frac{3x + 1}{1 - x}\))(\(\frac{x - 1}{1 - x}\))
= \(\frac{3x + 1}{x - 1}\)
Source: Myschool Past Questions Archive (Record #32434)