\(\left(\dfrac{1}{4}+\dfrac{4}{7}-\dfrac{5}{7}\right)\times\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}\right)\\ =\left(\dfrac{7}{28}+\dfrac{16}{28}-\dfrac{20}{28}\right)\times\left(\dfrac{6}{12}+\dfrac{4}{12}+\dfrac{3}{12}\right)\\ =\dfrac{3}{28}\times\dfrac{13}{12}\\ =\dfrac{13}{112}\)