đáng ra là toán lớp 6 đó nhưng mik thích đặt toán lớp 5 :)

A = \(\dfrac{10^{1990}+1}{10^{1991}+1}\) ⇒ 10A = \(\dfrac{10^{1991}+10}{10^{1991}+1}\) = \(1+\dfrac{9}{10^{1991}+1}\)

B =  \(\dfrac{10^{1991}+10}{10^{1992}+1}\) ⇒ 10B = \(\dfrac{10^{1992}+10}{10^{1992}+1}\) = 1 + \(\dfrac{9}{10^{1992}+1}\)

Vì \(\dfrac{9}{10^{1991}+1}\) > \(\dfrac{9}{10^{1992}+1}\)

10A > 10B => A > B

Giải:

Ta gọi \(\dfrac{10^{1990}+1}{10^{1991}+1}\) =A và \(\dfrac{10^{1991}}{10^{1992}}\) =B

Ta có:

A=\(\dfrac{10^{1990}+1}{10^{1991}+1}\) 

10A=\(\dfrac{10^{1991}+10}{10^{1991}+1}\) 

10A=\(\dfrac{10^{1991}+1+9}{10^{1991}+1}\) 

10A=\(1+\dfrac{9}{10^{1991}+1}\) 

Tương tự:

B=\(\dfrac{10^{1991}}{10^{1992}}\) 

10B=\(\dfrac{10^{1992}}{10^{1992}}=1\) 

Vì \(\dfrac{9}{10^{1991}+1}< 1\) nên 10A<10B

⇒ \(\dfrac{10^{1990}+1}{10^{1991}+1}\) < \(\dfrac{10^{1991}}{10^{1992}}\)

Áp dụng a/b < 1 => a/b < a+m/b+m (a;b;m thuộc N*)

=> \(B=\frac{10^{1991}+1}{10^{1992}+1}< \frac{10^{1991}+1+9}{10^{1992}+1+9}\)

=> \(B< \frac{10^{1991}+10}{10^{1992}+10}\)

=> \(B< \frac{10.\left(10^{1990}+1\right)}{10.\left(10^{1991}+1\right)}\)

=> \(B< \frac{10^{1990}+1}{10^{1991}+1}=A\)

=> B < A

Bài này mình biết làm nè , nhưng ... dài dòng lắm 

Bài này còn có cách khác 

Ta có : \(A=\frac{10^{1990}+1}{10^{1991}+1}=>10A=\frac{10.\left(10^{1990}+1\right)}{10^{1991}+1}\)

\(=>10A=\frac{10^{1991}+10}{10^{1991}+1}=\frac{\left(10^{1991}+1\right)+9}{10^{1991}+1}\)

\(=>10A=1+\frac{9}{10^{1991}+1}\)

Ta lại có : \(B=\frac{10^{1991}+1}{10^{1992}+1}=>10B=\frac{10.\left(10^{1991}+1\right)}{10^{1992}+1}\)

Tương tự như A => \(10B=1+\frac{9}{10^{1992}+1}\)

Vì \(\frac{9}{10^{1991}+1}>\frac{9}{10^{1992}+1}=>10A>10B\)

\(=>A>B\)

A < B

Chắc thế

:)

:)

đăt 10A=\(\frac{10^{1991}+1}{10^{1991}+1}\)=1+\(\frac{9}{10^{1991}}\)

Câu B tương tự 

ta có:\(\frac{9}{10^{1991}+1}\)>\(\frac{9}{10^{1992}}\)

nên 10A>10B

=>A>b

A=10^1990+1/10^1991

A=10.(10^1990+1 / 10^1991+1)

10A=10^1991+10 / 10^1991+1

10A=10^1991+1 / 10^1991+1 +9/10^1991+1

10A=1 + 9/10^1991

B=10^1991+1 / 10^1992+1

B=10.(10^1991+1 / 10^1992+1)

10B=10^1992+10 / 10^1992+1

10B=10^1992+1 / 10^1992+1 + 9/10^1992+1

10B= 1+9/10^1992+1

Ta có    9/10^1991 > 9/10^1992

                 10A     >     10B

                     A    >       B

Vì \(\frac{10^{1994}+1}{10^{1992}+1}\)<1

=> \(\frac{10^{1994}+1}{10^{1992}+1}\)<\(\frac{10^{1994}+1+9}{10^{1992}+1+9}\)

Ta có \(\frac{10^{1994}+1+9}{10^{1992}+1+9}\)=\(\frac{10\left(10^{1990}+1\right)}{10\left(10^{1991}+1\right)}\)=\(\frac{10^{1990}+1}{10^{1991}+2}\)

=>\(\frac{10^{1994}+1}{10^{1992}+1}\)<\(\frac{10^{1990}+1}{10^{1991}+2}\)

Vậy B < A

khó quá bạn