question_answer

If \[m=\frac{a+1}{a-1}\] and \[n=\frac{a-1}{a+1},\] then \[{{m}^{2}}+{{n}^{2}}-3\,mn\] is equal to:

A)  \[\frac{-\,{{a}^{4}}+18{{a}^{2}}-1}{{{a}^{4}}-2{{a}^{2}}+1}\]

B)  \[\frac{{{a}^{4}}-9{{a}^{2}}+3}{{{a}^{4}}+2{{a}^{2}}+1}\]

C)  \[\frac{{{a}^{4}}+9{{a}^{2}}-3}{{{a}^{4}}-2{{a}^{2}}+1}\]                 

D)  \[\frac{-\,{{a}^{4}}+16{{a}^{2}}+1}{{{a}^{4}}-2{{a}^{2}}+1}\]

E)  None of these