\(A=\frac{2.\left(1-\frac{1}{19}+\frac{1}{43}-\frac{1}{1943}\right)}{3.\left(1-\frac{1}{19}+\frac{1}{43}-\frac{1}{1943}\right)}:\frac{4\left(1-\frac{1}{29}+\frac{1}{41}-\frac{1}{2941}\right)}{5.\left(1-\frac{1}{29}+\frac{1}{41}-\frac{1}{2941}\right)}=\frac{2}{3}:\frac{4}{5}=\frac{2}{3}.\frac{5}{4}=\frac{5}{6}\)

Xin lỗi nha, mình chỉ biết làm bài này nhõn bằng cách qui đồng nhưng số lớn lắm!

\(A=\frac{2-\frac{2}{19}+\frac{2}{43}-\frac{2}{1995}}{3-\frac{3}{19}+\frac{3}{43}-\frac{3}{1995}}:\frac{4-\frac{4}{29}+\frac{4}{41}-\frac{4}{2941}}{5-\frac{5}{29}+\frac{5}{41}-\frac{5}{2941}}\)

\(\Rightarrow A=\frac{2\left(1-\frac{1}{19}+\frac{1}{43}-\frac{1}{1995}\right)}{3\left(1-\frac{1}{19}+\frac{1}{43}-\frac{1}{1995}\right)}:\frac{4\left(1-\frac{1}{29}+\frac{1}{41}-\frac{1}{2941}\right)}{5\left(1-\frac{1}{29}+\frac{1}{41}-\frac{1}{2941}\right)}\)

\(\Rightarrow A=\frac{2}{3}:\frac{4}{5}\)

\(\Rightarrow A=\frac{2}{3}.\frac{5}{4}\)

\(\Rightarrow A=\frac{10}{12}=\frac{5}{6}\)

thanks bạn

5/6 day 

HD: Vũ Phương Vy  em chỉ cần đặt ts c rồi rút gọn

ko chép lại đề nha

=\(A=\frac{2\left(1-\frac{2}{19}+\frac{2}{23}\right)-\frac{1}{1010}}{3\left(1-\frac{1}{19}+\frac{1}{23}-\frac{1}{2020}\right)}\)\(.\frac{4\left(1-\frac{1}{29}+\frac{1}{41}\right)-\frac{1}{505}}{5\left(1-\frac{1}{29}+\frac{1}{41}\right)-\frac{1}{404}}\)

rồi em chỉ cần rút gọn tiếp 

p/s đến đây thấy đề kì kì sao đó 

em chek lại đề đc k

đề đúng rồi đó ạ

đề đúng mà ko sai đâu nếu bạn ko tin thì xem bài 5 của đề này nhé : https://online-learning-izteach-aws-source-bucket.s3-ap-southeast-1.amazonaws.com/resource/49714800-4b02-11ea-a775-01bd84d6799a/4baf4091-c5ae-4d0f-819c-e9ee9eedd6a8/de-so-13-on-tap-va-cung-co-toan-6-pdf

\(A=\dfrac{5-\dfrac{5}{29}+\dfrac{5}{41}-\dfrac{5}{2941}}{3-\dfrac{3}{19}+\dfrac{3}{43}-\dfrac{3}{1943}}:\dfrac{4-\dfrac{4}{29}+\dfrac{4}{41}-\dfrac{4}{2941}}{2-\dfrac{2}{19}+\dfrac{2}{43}-\dfrac{2}{1943}}\)

\(=\dfrac{5-\dfrac{5}{29}+\dfrac{5}{41}-\dfrac{5}{2941}}{3-\dfrac{3}{19}+\dfrac{3}{43}-\dfrac{3}{1943}}.\dfrac{2-\dfrac{2}{19}+\dfrac{2}{43}-\dfrac{2}{1943}}{4-\dfrac{4}{29}+\dfrac{4}{41}-\dfrac{4}{2941}}\)

\(=\dfrac{5\left(1-\dfrac{1}{29}+\dfrac{1}{41}-\dfrac{1}{2941}\right)}{3\left(1-\dfrac{1}{19}+\dfrac{1}{43}-\dfrac{1}{1943}\right)}.\dfrac{2\left(1-\dfrac{1}{19}+\dfrac{1}{43}-\dfrac{1}{1943}\right)}{4\left(1-\dfrac{1}{29}+\dfrac{1}{41}-\dfrac{1}{2941}\right)}\)

\(=\dfrac{5}{3}.\dfrac{2}{4}=\dfrac{10}{12}=\dfrac{5}{6}\)

Vì đề bài không yêu cầu tính nên bn có thể không tính ra như mk cux đc!

Ta có:

\(A=\frac{2-\frac{2}{19}+\frac{2}{43}-\frac{2}{1943}}{3-\frac{3}{19}+\frac{3}{43}-\frac{3}{1943}}\)

\(A=\frac{2\left(1-\frac{1}{19}+\frac{1}{43}-\frac{1}{1943}\right)}{3\left(1-\frac{1}{19}+\frac{1}{43}-\frac{1}{1943}\right)}\)

\(A=\frac{2}{3}\)

Giúp Mik ik mai nộp oy

                            \(A=\frac{636363.37-373737.63}{1+2+3+...+2006}\)

                           \(A=\frac{63.10101.37-37.10101.63}{1+2+3+...+2006}\)

                         \(A=0\)

                    \(B=1\frac{6}{41}.\left(\frac{12+\frac{12}{19}-\frac{12}{37}-\frac{12}{53}}{3+\frac{3}{19}-\frac{3}{37}-\frac{3}{53}}:\frac{4+\frac{4}{17}+\frac{4}{19}+\frac{4}{2006}}{5+\frac{5}{17}+\frac{5}{19}+\frac{5}{2006}}\right).\frac{124242423}{237373735}\)

                 \(B=\frac{47}{41}.\left[\frac{4.\left(3+\frac{3}{19}-\frac{3}{37}-\frac{3}{53}\right)}{1.\left(3+\frac{3}{19}-\frac{3}{37}-\frac{3}{53}\right)}:\frac{4.\left(1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2006}\right)}{5.\left(1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2006}\right)}\right].\frac{124242423}{237373735}\)

                 \(B=\frac{47}{41}.\left(4:\frac{4}{5}\right).\frac{124242423}{237373735}\)

                 \(B=\frac{47}{41}.5.\frac{124242423}{237373735}\)

              \(B=\frac{47.5.124242423}{41.237373735}\)

              \(B=\frac{29196969405}{9732323135}\)

            Ủng hộ mk nha !!! ^_^

a) \(A=\frac{636363.37-373737.63}{1+2+3+...+2006}\)

\(A=\frac{10101.63.37-10101.37.63}{1+2+3+...+2006}\)

\(A=\frac{0}{1+2+3+...+2006}\)

\(A=0\)

b) \(B=1\frac{6}{41}\left(\frac{12+\frac{12}{19}-\frac{12}{37}-\frac{12}{53}}{3+\frac{3}{19}-\frac{3}{37}-\frac{3}{53}}.\frac{4+\frac{4}{17}+\frac{4}{19}+\frac{4}{2006}}{5+\frac{5}{17}+\frac{5}{19}+\frac{5}{2006}}\right).\frac{124242423}{237373735}\)

\(B=\frac{47}{41}.\frac{12}{3}.\left(\frac{1+\frac{1}{19}-\frac{1}{37}-\frac{1}{53}}{1+\frac{1}{19}-\frac{1}{37}-\frac{1}{53}}\right).\frac{4}{5}.\left(\frac{1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2006}}{1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2006}}\right).\frac{123}{235}\)

\(B=\frac{47.4.4.123}{41.5.235}\)

\(B=\frac{47.4.4.41.3}{41.5.47.5}\)

\(B=\frac{4.4.3}{5.5}\)

\(B=\frac{48}{25}\)

đặt \(S=\frac{2-\frac{2}{19}+\frac{2}{43}-\frac{2}{1943}}{3-\frac{3}{19}+\frac{3}{43}-\frac{3}{1943}};P=\frac{4-\frac{4}{29}+\frac{4}{41}-\frac{4}{2941}}{5-\frac{5}{29}+\frac{5}{41}-\frac{5}{2941}}\)

\(S=\frac{2-\frac{2}{19}+\frac{2}{43}-\frac{2}{1943}}{3-\frac{3}{19}+\frac{3}{43}-\frac{3}{1943}}=\frac{2\left(1-\frac{1}{19}+\frac{1}{43}-\frac{1}{1943}\right)}{3\left(1-\frac{1}{19}+\frac{1}{43}-\frac{1}{1943}\right)}=\frac{2}{3}\)

\(P=\frac{4-\frac{4}{29}+\frac{4}{41}-\frac{4}{2941}}{5-\frac{5}{29}+\frac{5}{41}-\frac{5}{2941}}=\frac{4\left(1-\frac{1}{29}+\frac{1}{41}-\frac{1}{2941}\right)}{5\left(1-\frac{1}{29}+\frac{1}{41}-\frac{1}{2941}\right)}=\frac{4}{5}\)

\(\Rightarrow A=S:P=\frac{2}{3}:\frac{4}{5}=\frac{2}{3}.\frac{5}{4}=\frac{10}{12}=\frac{5}{6}\)

vậy A=5/6
 

Ta có 2-2/19+2/43-2/1943=2.1-2.1/19+2.1/43-2.1/1943=2(1-1/19+1/43-1/1943)

Tương tự với 3 biểu thức còn lại , ta lại có : A=2/3:4/5=2/3.5/4=10/12=5/6