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The positive square root of \( \Large \left(x^{2}+2x-1\right)+\frac{1}{x^{2}+2x+1} \) is

A) \( \Large \left(x+1\right)+\frac{1}{ \left(x+1\right) } \)
B) \( \Large \left(x+1\right)-\frac{1}{ \left(x+1\right) } \)
C) \( \Large \left(x+2\right)-\frac{1}{ \left(x+1\right) } \)
D) \( \Large \left(x+2\right)+\frac{1}{ \left(x+1\right) } \)

Correct Answer:


B) \( \Large \left(x+1\right)-\frac{1}{ \left(x+1\right) } \)

Description for Correct answer:

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

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

Hence required positive square root

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

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

Part of solved Rational expression questions and answers : >> Elementary Mathematics >> Rational expression

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