question_answer

If \[\mathbf{x=}\frac{\sqrt{\mathbf{7}}\mathbf{+}\sqrt{\mathbf{5}}}{\sqrt{\mathbf{7}}\mathbf{-}\sqrt{\mathbf{5}}}\] and \[\mathbf{y=}\frac{\sqrt{\mathbf{7}}\mathbf{-}\sqrt{\mathbf{5}}}{\sqrt{\mathbf{7}}\mathbf{+}\sqrt{\mathbf{5}}}\], then find the value of \[\frac{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+xy+}{{\mathbf{y}}^{\mathbf{2}}}}{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-xy+}{{\mathbf{y}}^{\mathbf{2}}}}\]

A)  \[\frac{137}{143}\]                                                      

B)  \[\frac{143}{137}\]

C)  \[\frac{117}{128}\]                                                      

D)  \[\frac{128}{117}\]

E)  None of these