giúp với mọi người ơi

`4.`

So sánh `A = (10^9 + 1)/(10^10 + 1) ; B = (10^8 + 1)/(10^9 + 1)`

Ta có `:`

`A = (10^9 + 1)/(10^10 + 1) => 10A = (10(10^9 + 1))/(10^10 + 1) = (10^10 + 10)/(10^10 + 1) = (10^10 + 1 + 9)/(10^10 + 1) = 1 + 9/(10^10 + 1)`

`B = (10^8 + 1)/(10^9 + 1) => 10B = (10(10^8 + 1))/(10^9 + 1) = (10^9 + 10)/(10^10 + 1) = (10^9 + 1 + 9)/(10^9 + 1) = 1 + 9/(10^9 + 1)`

Vì `1 = 1 ; 9/(10^10 + 1) < 9/(10^9 + 1) => 1 + 9/(10^10 + 1) < 1 + 9/(10^9 + 1) => 10A < 10B => A < B`

Vậy `A < B`

_____________

`5.` 

So sánh `: A = (7^99 + 2)/(7^100 + 2) ; B = (7^98 + 2)/(7^99 + 2)`

Ta có `:`

`A = (7^99 + 2)/(7^100 + 2) => 7A = (7(7^99 + 2))/(7^100 + 2) = (7^100 + 14)/(7^100 + 2) = (7^100 + 2 + 12)/(7^100 + 2) = 1 + 12/(7^100 + 2)`

`B = (7^98 + 2)/(7^99 + 2) => 7A = (7(7^98 + 2))/(7^99 + 2) = (7^99 + 14)/(7^99 + 2) = (7^9 + 2 + 12)/(7^99 + 2) = 1 + 12/(7^99 + 2)`

Vì `1 = 1 ; 12/(7^100 + 2) < 12/(7^99 + 2) => 1 + 7/(7^100 + 2) < 1 + 7/(7^99 + 2) => 7A < 7B => A < B`

Vậy `A < B`

#Robbery