a: Đặt a=5741; b=3759
\(A=4\frac{7}{5741}\cdot\frac{1}{3759}-\frac{4}{3759}\cdot1\frac{2}{5741}+\frac{1}{3759}+\frac{1}{3759\cdot5741}\)
\(=\left(4+\frac{7}{a}\right)\cdot\frac{1}{b}-\frac{4}{b}\cdot\left(1+\frac{2}{a}\right)+\frac{1}{b}+\frac{1}{ab}\)
\(=\frac{4a+7}{a}\cdot\frac{1}{b}-\frac{4}{b}\cdot\frac{a+2}{a}+\frac{a}{ab}+\frac{1}{ab}=\frac{4a+7-4a-8+a+1}{ab}=\frac{a}{ab}=\frac{1}{b}\)
\(=\frac{1}{3759}\)
b: Đặt a=3150; b=6517
\(B=2\frac{1}{3150}\cdot\frac{3}{6517}-\frac{1}{1050}\cdot3\frac{6516}{6517}+\frac{4}{1050}-\frac{6}{3150\cdot6517}\)
\(=\left(2+\frac{1}{a}\right)\cdot\frac{3}{b}-\frac{3}{a}\cdot\left(3+\frac{b-1}{b}\right)+\frac{12}{a}-\frac{6}{ab}\)
\(=\frac{2a+1}{a}\cdot\frac{3}{b}-\frac{3}{a}\cdot\frac{3b+b-1}{b}+\frac{12b}{ab}-\frac{6}{ab}\)
\(=\frac{6a+3-12b+3+12b-6}{ab}=\frac{6a}{ab}=\frac{6}{b}=\frac{6}{6517}\)
