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The sum $1/ (x - 1) + 1/ (x + 1)$ simplifies to:

Competition practiceAlgebra

A $2/ (x^{2} - 1)$
B $2 x / (x^{2} - 1)$
C $2 x / (x^{2} + 1)$
D $x / (x^{2} - 1)$

Step-by-Step Solution

Take the common denominator

(x - 1) (x + 1) = x^{2} - 1

. The numerator becomes

(x + 1) + (x - 1) = 2 x

, so the sum is

2 x / (x^{2} - 1)

.

Answer: B)

2 x / (x^{2} - 1)

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