Giải thích các bước giải:

A = $\frac{4}{7.31}$ + $\frac{6}{7.41}$ + $\frac{9}{10.41}$ + $\frac{7}{10.57}$ 

⇒ A =  $\frac{20}{35.31}$ + $\frac{30}{35.41}$ + $\frac{45}{50.41}$ + $\frac{35}{50.57}$ 

⇒ A = 5 . ($\frac{4}{35.31}$ + $\frac{6}{35.41}$ + $\frac{9}{50.41}$ + $\frac{7}{50.57}$)

⇒ A = 5 . ( $\frac{1}{31}$ - $\frac{1}{35}$ + $\frac{1}{35}$ - $\frac{1}{41}$ + $\frac{1}{41}$ - $\frac{1}{50}$ + $\frac{1}{50}$ - $\frac{1}{57}$ )

⇒ A = 5 .($\frac{1}{31}$ - $\frac{1}{57}$)  (1)

B=7/(19x31)+5/(19x43)+3/(23x43)+11/(23x57)

⇒ B = 2 . ($\frac{7}{38.31}$ + $\frac{5}{38.43}$ + $\frac{3}{43.46}$ + $\frac{11}{46.57}$ )

⇒ B = 2 . ($\frac{1}{31}$ - $\frac{1}{38}$ + $\frac{1}{38}$ - $\frac{1}{43}$ + $\frac{1}{43}$ - $\frac{1}{46}$ + $\frac{1}{46}$ - $\frac{1}{57}$ )

⇒ B = 2 . ($\frac{1}{31}$ - $\frac{1}{57}$) (2)
Từ (1) và (2) => $\frac{A}{B}$ = $\frac{5}{2}$ 

Đáp án:

$\rm\dfrac{A}{B}=\dfrac{5}{2}$

Giải thích các bước giải:

a) `text(A)=4/(7.31)+6/(7.41)+9/(10.41)+7/(10.57)`

`=>text(A)=(4.5)/(5.7.31)+(5.6)/(5.7.41)+(5.9)/(5.10.41)+(7.5)/(5.10.57)`

`=>text(A)=(4.5)/31.35+(5.6)/35.41+(5.9)/41.50+(5.7)/(50.57`

`=>text(A)/5=4/31.35+6/35.41+9/41.50+7/50.57`

`=>text(A)/5=1/31-1/35+1/35-1/41+1/41-1/50+1/50-1/57`

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

`=>text(A)/5=26/1767`

`=>text(A)=130/1767`

`=>text(B)=7/(19.31)+5/(19.43)+3/(23.43)+11/(23.57)`

`=>text(B)=(7.2)/(2.19.31)+(2.5)/(2.19.43)+(2.3)/(2.23.43)+(2.11)/(2.23.57)`

`=>text(B)=(7.2)/(31.38)+(2.5)/(38.43)+(2.3)/(43.46)+(2.11)/(46.57)`

`=>text(B)/2=7/31.38+5/38.43+3/43.46+11/46.57`

`=>text(B)/2=1/31-1/38+1/38-1/43+1/43-1/46+1/46-1/57`

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

`=>text(B)/2=26/1767`

`=>text(B)=52/1767`

`=>`$\rm\dfrac{A}{B}=\dfrac{\dfrac{130}{1767}}{\dfrac{52}{1767}}=\dfrac{5}{2}$

Vậy $\rm\dfrac{A}{B}=\dfrac{5}{2}$.