Express \(\frac{1}{x + 1}\) - \(\frac{1}{x - 2}\) as a single algebraic fraction
A
\(\frac{-3}{(x + 1)(2 - x)}\)
B
\(\frac{3}{(x + 1)(2 - x)}\)
C
\(\frac{-1}{(x + 1)}\)
D
\(\frac{1}{(x + 1)(x - 2)}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{1}{x + 1}\) - \(\frac{1}{x - 2}\) = \(\frac{x - 2 - x - 1}{(x + 1)(x - 2)}\)
= \(\frac{-3}{(x + 1)(2 - x)}\)
Source: Myschool Past Questions Archive (Record #31553)