\(A=\dfrac{7}{19}.\dfrac{8}{11}+\dfrac{7}{19}.\dfrac{3}{11}+\dfrac{12}{19}\)
\(A= \dfrac{7}{19}.\left (\dfrac{8}{11}+\dfrac{3}{11} \right )+\dfrac{12}{19}\)
\(A = \dfrac{7}{{19}}.\dfrac{{11}}{{11}} + \dfrac{{12}}{{19}}\)
\(A=\dfrac{7}{19}.1 +\dfrac{12}{19}=1\).
\(B= \dfrac{5}{9}.\dfrac{7}{13}+\dfrac{5}{9}.\dfrac{9}{13}-\dfrac{5}{9}.\dfrac{3}{13}\)
\(B=\dfrac{5}{9}.\left (\dfrac{7}{13}+\dfrac{9}{13}-\dfrac{3}{13} \right )\)
\(B=\dfrac{5}{9}.\dfrac{7+9-3}{13}\)
\(B=\dfrac{5}{9}.\dfrac{13}{13}=\dfrac{5}{9}.1=\dfrac{5}{9}\)
\(C=\left (\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117} \right ).\left (\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12} \right )\)
\(C=\left (\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117} \right ).\dfrac{4-3-1}{12}\)
\(C=\left (\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117} \right ).0=0\)
