\(\dfrac{27}{23}+\dfrac{5}{21}-\dfrac{4}{23}+\dfrac{6}{21}-\dfrac{1}{2}\)
\(=\left(\dfrac{27}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{6}{21}\right)-\dfrac{1}{2}\)
\(=1+\dfrac{11}{21}-\dfrac{1}{2}\)
\(=\dfrac{32}{21}-\dfrac{1}{2}\)
\(=\dfrac{43}{42}\)