`a)` Ta có :

`237/142=(142+95)/142=142/142+95/142=1+95/142`

`246/151=(151+95)/151=151/151+95/151=1+95/151`

Do `95/142>95/151`

`=>1+95/142>1+95/151`

`=>237/142>246/151`

Vậy `237/142>246/151`

`b)` Ta có :

`A=(98^99 +1)/(98^89 +1)`

`=>1/(98^10)A=(98^99 +1)/(98^89 +1). 1/(98^10)`

`=>1/(98^10)A=(1(98^99 +1))/(98^10 (98^89+1))`

`=>1/(98^10)A=(98^99 +1)/(98^99 +98^10)`

`=>1/(98^10)A=(98^99 +98^10 -98^10 +1)/(98^99 +98^10)`

`=>1/(98^10 )A=(98^99 +98^10)/(98^99 +98^10)-(98^10 -1)/(98^99 +98^10)`

`=>1/(98^10)A=1-(98^10 -1)/(98^99 +98^10)`

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`B=(98^98 +1)/(98^88 +1)`

`=>1/(98^10)B=(98^98 +1)/(98^88 +1). 1/(98^10)`

`=>1/(98^10)B=(1(98^98 +1))/(98^10 (98^88+1))`

`=>1/(98^10)B=(98^98 +1)/(98^98 +98^10)`

`=>1/(98^10)B=(98^98 +98^10 -98^10 +1)/(98^98 +98^10)`

`=>1/(98^10 )B=(98^98 +98^10)/(98^98 +98^10)-(98^10 -1)/(98^98 +98^10)`

`=>1/(98^10)B=1-(98^10 -1)/(98^98 +98^10)`

Do `(98^10 -1)/(98^99 +98^10)<(98^10 -1)/(98^98 +98^10)`

`=>1-(98^10 -1)/(98^99 +98^10)>1-(98^10 -1)/(98^98 +98^10)`

`=>1/(98^10)A>1/(98^10)B`

`=>A>B`

Vậy `A>B`

Đáp án:  Câu a phân số 237/142 < 246/ 151 vì 237+9/151+9 = 246/151

               câu B A>B 

 

Giải thích các bước giải: câu B do A= 98 mũ 99 +1 phần 98 mũ 89+1 >1 nên A= 98 mũ 99+1 phần 98 mũ 89 +1> 98 mũ 99 +1+97 phần 98 mũ 89 +1+ 97 = 98 (98 mũ 98 +1) phần 98 ( 98 mũ 88+1)

= 98 mũ 98+1 phần 98 mũ 88 =B 

suy ra A>B