Write as a single fraction \(\frac{1}{1 - x} + \frac{2}{1 + x}\)
A
\(\frac{x + 3}{1 - x^2}\)
B
\(\frac{3 - x}{(1 - x)^2}\)
C
\(\frac{3 - x}{1 + x^2}\)
D
\(\frac{3 - x}{(1 + x)^2}\)
E
\(\frac{3 - x}{1 - x^2}\)
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
\(\frac{1}{1 - x} + \frac{2}{1 + x}\)
= \(\frac{(1 + x) + 2(1 - x)}{(1 - x)(1 + x)}\)
= \(\frac{1 + x + 2 - 2x}{1 - x^2}\)
= \(\frac{3 - x}{1 - x^2}\)
Source: Myschool Past Questions Archive (Record #23149)