Question

[Nguyễn Huy Hoàng 2]

Tính \(A=\left(\frac{112}{13.20}+\frac{112}{20.27}+...+\frac{112}{62.69}\right)\div\)\(\left(\frac{-5}{9.13}-\frac{7}{9.25}-\frac{13}{19.25}-\frac{31}{19.69}\right)\)

Answer 1

[Trịnh Đức Minh]

Ta có: \(\left(\frac{112}{13.20}+\frac{112}{20.27}+...+\frac{112}{62.69}\right)\)

=\(\left(\frac{112}{13}-\frac{112}{20}+\frac{112}{20}-\frac{112}{27}+...+\frac{112}{62}-\frac{112}{69}\right)\)

112 là tử chung

=>\(112\cdot\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+...+\frac{1}{62}-\frac{1}{69}\right)\)

Rút gọn các phân số cho nhau, ta còn:

\(112.\left(\frac{1}{13}-\frac{1}{69}\right)\)=\(112\cdot\frac{56}{897}=\frac{6272}{897}\)(1)

Ta có: \(\left(\frac{-5}{9\cdot13}-\frac{7}{9\cdot25}-\frac{13}{19\cdot25}-\frac{31}{19\cdot69}\right)\)=\(\left(-\frac{24}{325}-\frac{122}{32775}\right)\)=\(\left(-\frac{1322}{17043}\right)\)(2)

(1);(2) => \(A=\)\(\frac{6272}{897}\)\(:\left(-\frac{1322}{17043}\right)\)\(\)\(=\)\(-\frac{59584}{661}\)

C