The sum of (x - 1/x + 1) and its reciprocal is ……………
The sum of \((\frac{x-1}{x+1})\) and its reciprocal is ………………
A) \(\frac{x^2+1}{x^2-1}\)
B) \(\frac{2(x^2+1)}{x^2-1}\)
C) \(\frac{x^2-1}{x^2+1}\)
D) \(\frac{2(x^2-1)}{x^2+1}\)
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Correct option is (B) \(\frac{2(x^2+1)}{x^2-1}\)
Sum of \(\left(\frac{x-1}{x+1}\right)\) and its reciprocal \(=\frac{x-1}{x+1}+\frac{x+1}{x-1}\)
\(=\frac{(x-1)^2+(x+1)^2}{(x+1)(x-1)}\) \(=\frac{(x^2-2x+1)+(x^2+2x+1)}{x^2-1}\)
\(=\frac{2(x^2+1)}{x^2-1}\)
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