\( A = \left( {\dfrac{{{x^2} + 1}}{{{x^2} + x}} + \dfrac{2}{{x + 1}}} \right):\dfrac{{{{\left( {x + 1} \right)}^2}}}{{2x}}\\ A = \left[ {\dfrac{{{x^2} + 1}}{{x\left( {x + 1} \right)}} + \dfrac{2}{{x + 1}}} \right].\dfrac{{2x}}{{{{\left( {x + 1} \right)}^2}}}\\ A = \dfrac{{{x^2} + 2x + 1}}{{x\left( {x + 1} \right)}}.\dfrac{{2x}}{{{{\left( {x + 1} \right)}^2}}}\\ A = \dfrac{{{{\left( {x + 1} \right)}^2}}}{{x\left( {x + 1} \right)}}.\dfrac{{2x}}{{{{\left( {x + 1} \right)}^2}}} = \dfrac{2}{{x + 1}} \)
