The sum of \((\frac{x-1}{x+1})\) and its reciprocal is …………�

1.	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) \(\frac{2(x^2-1)}{x^2+1}\)
Answer» Correct option is (B) \(\frac{2(x^2+1)}{x^2-1}\) Sum of \(\left(\frac{x-1}{x+1}\right)\) and its reciprocal \(=\frac{x-1}{x+1}+\frac{x+1}{x-1}\) \(=\frac{(x-1)^2+(x+1)^2}{(x+1)(x-1)}\) \(=\frac{(x^2-2x+1)+(x^2+2x+1)}{x^2-1}\) \(=\frac{2(x^2+1)}{x^2-1}\) Correct option is B) \(\frac{2(x^2+1)}{x^2-1}\)

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) \(\frac{2(x^2-1)}{x^2+1}\)

Answer»

Correct option is (B) \(\frac{2(x^2+1)}{x^2-1}\)

Sum of \(\left(\frac{x-1}{x+1}\right)\) and its reciprocal \(=\frac{x-1}{x+1}+\frac{x+1}{x-1}\)

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

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

Correct option is B) \(\frac{2(x^2+1)}{x^2-1}\)