a) \(\frac{42}{-37}=-\frac{42}{37}=-\frac{37+5}{37}=-1-\frac{5}{37}\) ; \(-\frac{56}{43}=-\frac{43+13}{43}=-1-\frac{13}{43}\)

So sánh \(\frac{5}{37}\) với \(\frac{13}{43}\) thì dễ dàng được \(\frac{5}{37}< \frac{13}{43}\)

Do đó \(\frac{42}{-37}>\frac{-56}{43}\)

b) Dễ thấy \(\frac{37}{67}>0>-\frac{377}{677}\)

Ta có\(71^{50}=71^{2.25}=\left(71^2\right)^{25}=5041^{25}\) 

\(37^{75}=37^{3.25}=\left(37^3\right)^{25}=50653^{25}\)

Mà 50653²⁵ > 5041²⁵

suy ra \(37^{75}>71^{50}\)

Ta có : 71⁵⁰ = 71^{2 . 25} = (71²) ²⁵ = 5041²⁵

          37⁷⁵ = 37 ^{3 . 25} = (37³ ) ²⁵ = 50653²⁵

Vì 5041²⁵ < 50653²⁵

nên  71⁵⁰ < 37⁷⁵

           Vậy 71⁵⁰ < 37⁷⁵

#HOK TỐT#

\(37^{75}>32^{75}=\left(2^5\right)^{75}=2^{375}>2^{350}=128^{50}>71^{50}\)

\(\dfrac{55}{57}< 1< \dfrac{89}{43}\)

\(\Rightarrow\dfrac{55}{57}< \dfrac{89}{43}\)

31¹¹<32¹¹=2⁵⁵

17¹⁴>16¹⁴=2⁵⁶

=>Vì 2⁵⁵<2⁵⁶ nên 31¹¹<17¹⁴.

kết quả : A > B

Ta có: 
7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80 

1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 = (1/41 + 1/42 + 1/43 + ...+ 1/60) + (1/61 + 1/62 +...+ 1/79 + 1/80) 

Do 1/41> 1/42 > 1/43 > ...>1/59 > 1/60 
=> (1/41 + 1/42 + 1/43 + ...+ 1/60) > 1/60 + ...+ 1/60 = 20/60 

và 1/61> 1/62> ... >1/79> 1/80 
=> (1/61 + 1/62 +...+ 1/79 + 1/80) > 1/80 + ...+ 1/80 = 20/80 

Vậy: 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 20/60 + 20/80 = 7/12 

=> 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 7/12

\(A>B\)

Cảm ơn các bạn nha!