Simplify \( \frac{1}{(x + 1)} + \frac{1}{(x − 1)} \)
A
2x/(x + 1)(x−3)
B
2x/(x + 1)(x−1)
C
2x/(x + 1)2
D
2x(x+1)2
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
[1 \div (x+1)] + [1 \div (x − 1)]
= ((x − 1) + [(x + 1)) \div (x+1)(x − 1)]
Using the L.C.M.
= (x − 1 + x + 1) \div (x + 1)(x − 1)
= (x + 2 − 1 + 1) \div (x + 1)(x − 1)
= 2x \div (x + 1)(x − 1) =2x \div (x + 1)(x − 1)
Source: Myschool Past Questions Archive (Record #41284)