\(A=\dfrac{\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{9}}{\dfrac{4}{3}+\dfrac{4}{5}-\dfrac{4}{9}}\\ =\dfrac{\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{9}}{2.\left(\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{9}\right)}\\ =\dfrac{1}{2}\)
\(A=\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{9}=\dfrac{2.15+2.9-2.5}{45}=\dfrac{30+18-10}{45}=\dfrac{38}{45}\\ B=\dfrac{4}{3}+\dfrac{4}{5}-\dfrac{4}{9}=\dfrac{4.15+4.9-4.5}{45}=\dfrac{60+36-20}{45}=\dfrac{76}{45}\\ \Rightarrow A:B=\dfrac{38}{45}:\dfrac{76}{45}=\dfrac{38}{76}=\dfrac{1}{2}\)
\(A=\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{9}=\dfrac{16}{15}-\dfrac{2}{9}=\dfrac{38}{45}\)
\(\dfrac{4}{3}+\dfrac{4}{5}-\dfrac{4}{9}=\dfrac{32}{15}-\dfrac{4}{9}=\dfrac{76}{45}\)
