\(D=\dfrac{1}{1-\dfrac{1}{1-2^2}}+\dfrac{1}{1+\dfrac{1}{1+2^2}}\)
\(D=\dfrac{1}{1-\dfrac{1}{1-4}}+\dfrac{1}{1+\dfrac{1}{1+4}}\)
\(D=\dfrac{1}{1+\dfrac{1}{3}}+\dfrac{1}{1+\dfrac{1}{5}}\)
\(D=1:\left(1+\dfrac{1}{3}\right)+1:\left(1+\dfrac{1}{5}\right)\)
\(D=1:\dfrac{4}{3}+1:\dfrac{6}{5}\)
\(D=1.\dfrac{3}{4}+1.\dfrac{5}{6}\)
\(D=1.\left(\dfrac{3}{4}+\dfrac{5}{6}\right)\)
\(D=\dfrac{19}{12}\)
\(D=\dfrac{1}{1-\dfrac{1}{1-2^2}}+\dfrac{1}{1+\dfrac{1}{1+2^2}}\)
\(=\dfrac{1}{\dfrac{\left(1-2^2\right)-1}{1-2^2}}+\dfrac{1}{\dfrac{\left(1+2^2\right)+1}{1+2^2}}\)
\(=\dfrac{1}{\dfrac{-2^2}{1-2^2}}+\dfrac{1}{\dfrac{2+2^2}{1+2^2}}\)
\(=\dfrac{1-2^2}{-2^2}+\dfrac{1+2^2}{2+2^2}\)
\(=\dfrac{2^2-1}{2^2}+\dfrac{2^2+1}{2^2+2}\)
\(=\dfrac{2^2}{2^2}-\dfrac{1}{2^2}+\dfrac{2^2+2}{2^2+2}-\dfrac{1}{2^2+2}\)
\(=1+1-\left(\dfrac{1}{2^2}+\dfrac{1}{2^2+2}\right)\)
\(=2-\left[\dfrac{1}{2^2}+\dfrac{1}{2\left(2+1\right)}\right]\)
\(=2-\dfrac{\left(2+1\right)+2}{2^2\left(2+1\right)}\)
\(=2-\dfrac{5}{2^2.3}\)
\(=\dfrac{2^3.3-5}{2^2.3}\)
\(=\dfrac{8.3-5}{4.3}\)
\(=\dfrac{24-5}{12}\)
\(=\dfrac{19}{12}\)
