Question

Tính nhanh:

B=\(2\dfrac{1}{3154}\cdot\dfrac{3}{6517}-\dfrac{3}{3154}\cdot\dfrac{6516}{6517}+\dfrac{6}{1577}-\dfrac{6}{3154\cdot6517}\)

Answer 1

Đặt 3154=a; 6517=b

Theo đề, ta có:

\(B=2\dfrac{1}{a}\cdot\dfrac{3}{b}-\dfrac{3}{a}\cdot\dfrac{b-1}{b}+\dfrac{6}{\dfrac{1}{2}a}-\dfrac{6}{a\cdot b}\)

\(=\dfrac{2a+1}{a}\cdot\dfrac{3}{b}-\dfrac{3b-3}{ab}+\dfrac{12}{a}-\dfrac{6}{a\cdot b}\)

\(=\dfrac{6a+3-3b+3-6}{ab}+\dfrac{12b}{ab}\)

\(=\dfrac{6a-3b+12b}{ab}=\dfrac{6a+9b}{ab}=\dfrac{3\left(2a+3b\right)}{ab}\)

\(=\dfrac{3\left(2\cdot3154+3\cdot6517\right)}{3154\cdot6517}\)