\(A=\dfrac{4}{7.31}+\dfrac{6}{7.41}+\dfrac{9}{10.41}+\dfrac{7}{10.57}\Rightarrow\dfrac{A}{5}=\dfrac{4}{35.31}+\dfrac{6}{35.41}+\dfrac{9}{50.41}+\dfrac{7}{50.57}\)

\(\dfrac{A}{5}=\dfrac{1}{31}-\dfrac{1}{35}+\dfrac{1}{35}-\dfrac{1}{41}+\dfrac{1}{41}-\dfrac{1}{50}+\dfrac{1}{50}-\dfrac{1}{57}\)

\(\dfrac{A}{5}=\dfrac{1}{31}-\dfrac{1}{57}=\dfrac{26}{31.57}\Rightarrow A=\dfrac{130}{31.57}\)

\(\dfrac{B}{2}=\dfrac{7}{38.31}+\dfrac{5}{38.41}+\dfrac{3}{46.43}+\dfrac{11}{46.57}\Rightarrow\dfrac{B}{2}=\dfrac{1}{31}-\dfrac{1}{57}=\dfrac{26}{31.57}\)

\(\Rightarrow B=\dfrac{52}{31.57}\)

\(\dfrac{A}{B}=\dfrac{130}{31.51}:\dfrac{52}{31.57}=\dfrac{5}{2}\)

Ta có : `A:5=4/35.31+6/35.41++9/50.41+7/50.57`

`A/5 = 1/31 - 1/35 +1/35-1/41+1/41-1/50+1/50-1/57`

`A/5 =1/31-1/57` `(1)`

Lại có : `B:2=7/38.31 +5/38.43+3/46.43+11/46.57`

`B/2 =1/31-1/38+1/38-1/43+1/43-1/46+1/46-1/57`

`B/2 =1/31-1/57` `(2)`

Từ `(1)` và `(2)` `=>A/5 =B/2`

                         `=>A/B=5/2`

a) Ta có: \(A=\dfrac{4}{7\cdot31}+\dfrac{6}{7\cdot41}+\dfrac{9}{10\cdot41}+\dfrac{7}{10\cdot57}\)

\(=\dfrac{20}{31\cdot35}+\dfrac{30}{35\cdot41}+\dfrac{45}{41\cdot50}+\dfrac{35}{50\cdot57}\)

\(=5\left(\dfrac{4}{31\cdot35}+\dfrac{6}{35\cdot41}+\dfrac{9}{41\cdot50}+\dfrac{7}{50\cdot57}\right)\)

\(=5\left(\dfrac{1}{31}-\dfrac{1}{35}+\dfrac{1}{35}-\dfrac{1}{41}+\dfrac{1}{41}-\dfrac{1}{50}+\dfrac{1}{50}-\dfrac{1}{57}\right)\)

\(=5\left(\dfrac{1}{31}-\dfrac{1}{57}\right)\)

Ta có: \(B=\dfrac{7}{19\cdot31}+\dfrac{5}{19\cdot43}+\dfrac{3}{23\cdot43}+\dfrac{11}{23\cdot57}\)

\(=\dfrac{14}{31\cdot38}+\dfrac{10}{38\cdot43}+\dfrac{6}{43\cdot46}+\dfrac{22}{46\cdot57}\)

\(=2\left(\dfrac{7}{31\cdot38}+\dfrac{5}{38\cdot43}+\dfrac{3}{43\cdot46}+\dfrac{11}{46\cdot57}\right)\)

\(=2\left(\dfrac{1}{31}-\dfrac{1}{38}+\dfrac{1}{38}-\dfrac{1}{43}+\dfrac{1}{43}-\dfrac{1}{46}+\dfrac{1}{46}-\dfrac{1}{57}\right)\)

\(=2\left(\dfrac{1}{31}-\dfrac{1}{57}\right)\)

Suy ra: \(\dfrac{A}{B}=\dfrac{5\left(\dfrac{1}{31}-\dfrac{1}{57}\right)}{2\left(\dfrac{1}{31}-\dfrac{1}{57}\right)}=\dfrac{5}{2}\)

ko bít

giúp mình với mai thi rùi

\(\left(\frac{7}{19.31}+\frac{5}{19.43}+\frac{3}{23.43}+\frac{11}{23.57}\right):\left(\frac{1}{31}-\frac{1}{57}\right)\)

\(=\frac{7}{19}.\frac{7}{31}+\frac{5}{19}.\frac{5}{43}+\frac{3}{23}.\frac{3}{43}+\frac{11}{23}.\frac{11}{57}:\frac{1}{31}-\frac{1}{57}\)

\(=\frac{7}{19}+\frac{5}{19}.\frac{7}{31}+\frac{1}{31}:\frac{5}{43}-\frac{3}{43}.\frac{3}{23}+\frac{11}{23}.\frac{11}{57}+\frac{1}{57}\)

\(=\frac{12}{19}.\frac{8}{31}:\frac{2}{43}.\frac{7}{16}.\frac{4}{19}\)

\(=\frac{1204}{1767}\)

B=7/(19.31)+5/(19.43)+3/(23.43) 
+11/(23.57) 
Ta nhân cả tử và mẫu của các phân số biểu thức B với 2 
=>B=2(1/31-1/57) 
=>A/B=5/2

sai rùi bn

 A=4/(7.31)+6/(7.41)+9/(10.41)+7/(10.51) 
=20/(35.31)+30/(35.41)+45/(50.41) 
+35/(50.51) 
=5[4/(35.31)+6/(35.41)+9/(50.41) 
+7/(50.51)] 
=5(1/31-1/35+1/35-1/41+1/41-1/50 
+1/50-1/57) 
=5(1/31-1/57) 
B=7/(19.31)+5/(19.43)+3/(23.43) 
+11/(23.57) 
tương tự chưng minh như biểu thức A ta nhân cả tử và mẫu của các phân số biểu thức B với 2 
=>B=2(1/31-1/57) 
=>A/B=5/2

vậy B=5/2