Đáp án:
A=1
Giải thích các bước giải:
\(\begin{array}{*{20}{l}}
{A = \dfrac{1}{{2 + 2\sqrt x }} + \dfrac{1}{{2 - 2\sqrt x }} - \dfrac{{{x^2} + 1}}{{1 - {x^2}}}}\\
{{\rm{\;}} = \dfrac{1}{{2\left( {1 + \sqrt x } \right)}} + \dfrac{1}{{2\left( {1 - \sqrt x } \right)}} - \dfrac{{2\left( {{x^2} + 1} \right)}}{{2\left( {1 - \sqrt x } \right)\left( {1 + \sqrt x } \right)}}}\\
{ = \dfrac{{1 - \sqrt x {\rm{ \;}} + 1 + \sqrt x {\rm{ \;}} - 2{x^2} - 2}}{{2\left( {1 - \sqrt x } \right)\left( {1 + \sqrt x } \right)}}}\\
{{\rm{\;}} = \dfrac{{ - 2{x^2} + 2}}{{2\left( {1 - \sqrt x } \right)\left( {1 + \sqrt x } \right)}}}\\
{ = {\rm{ \;}} - \dfrac{{2\left( {{x^2} - 1} \right)}}{{2\left( {1 - \sqrt x } \right)\left( {1 + \sqrt x } \right)}}}\\
{ = \dfrac{{2\left( {1 - {x^2}} \right)}}{{2\left( {1 - {x^2}} \right)}} = 1}
\end{array}\)
