Question

Cho biểu thức:

 \(A=\frac{4}{7.31}+\frac{6}{7.41}+\frac{9}{10.41}+\frac{7}{10.57}\)   \(B=\frac{7}{19.31}+\frac{5}{19.43}+\frac{3}{23.43}+\frac{11}{23.57}\)

Tính tỉ số \(\frac{A}{B}\)

Ai nhanh mik tick nha, mik can gap!!

Answer 1

Ta có: 

\(\frac{A}{5}=\frac{4}{35\cdot31}+\frac{6}{35\cdot41}+\frac{9}{50\cdot41}+\frac{7}{50\cdot57}=\frac{35-31}{35\cdot31}+\frac{41-35}{35\cdot41}+\frac{50-41}{50\cdot41}+\frac{57-50}{50\cdot57}\)    ( Ps cuối là\(\frac{57-50}{50.57}\) nha).

\(=\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{41}+\frac{1}{41}-\frac{1}{50}+\frac{1}{50}-\frac{1}{57}\) 

\(\Rightarrow\frac{A}{5}=5\cdot\left(\frac{1}{31}-\frac{1}{57}\right)\) 

Tương tự:

\(\frac{B}{2}=\frac{7}{38.31}+\frac{5}{38.43}+\frac{3}{43.46}+\frac{11}{46.57}=\frac{38-31}{38.31}+\frac{41-38}{38.41}+\frac{46-43}{43.46}+\frac{57-46}{46.57}\) 

\(=\frac{1}{31}-\frac{1}{38}+\frac{1}{38}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}+\frac{1}{46}-\frac{1}{57}\) 

\(\Rightarrow\frac{B}{2}=2\cdot\left(\frac{1}{31}-\frac{1}{57}\right)\) 

Từ đó, suy ra:

\(\frac{A}{B}=\frac{5}{2}\) 

Vậy \(\frac{A}{B}=\frac{5}{2}\)

Answer 2

P/s: Có gì thừa hay thiếu thì bạn thêm hoặc bớt đi nha.

~Hk tốt~