A) \[{{a}^{2}}\]
B) \[{{b}^{2}}\]
C) \[{{a}^{2}}-{{b}^{2}}\]
D) \[\frac{4{{a}^{2}}-2{{b}^{2}}}{{{b}^{2}}}\]
Correct Answer: B
Solution :
We have, \[\frac{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}+\frac{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}\] \[=\frac{{{(a+\sqrt{{{a}^{2}}-{{b}^{2}}})}^{2}}+{{(a-\sqrt{{{a}^{2}}-{{b}^{2}}})}^{2}}}{{{a}^{2}}-{{(\sqrt{{{a}^{2}}-{{b}^{2}}})}^{2}}}\] \[{{a}^{2}}+{{a}^{2}}-{{b}^{2}}+2a\sqrt{{{a}^{2}}-{{b}^{2}}}+{{a}^{2}}+{{a}^{2}}\] \[=\frac{-{{b}^{2}}-2a\sqrt{{{a}^{2}}-{{b}^{2}}}}{{{a}^{2}}-{{a}^{2}}+{{b}^{2}}}\] \[=\frac{4{{a}^{2}}-2{{b}^{2}}}{{{b}^{2}}}\] \[\therefore \]The denomination of the given expression is \[{{b}^{2}}\]
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