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

a,A<B

b,A,<B

c,A<B

a, \(A-B=\frac{3}{8^3}+\frac{7}{8^4}-\frac{7}{8^3}-\frac{3}{8^4}==\left(\frac{7}{8^4}-\frac{3}{8^4}\right)-\left(\frac{7}{8^3}-\frac{3}{8^3}\right)=\frac{4}{8^4}-\frac{4}{8^3}< 0\)

Vậy A < B

b, \(A=\frac{10^7+5}{10^7-8}=\frac{10^7-8+13}{10^7-8}=1+\frac{13}{10^7-8}\)

\(B=\frac{10^8+6}{10^8-7}=\frac{10^8-7+13}{10^8-7}=1+\frac{13}{10^8-7}\)

Vì \(10^7-8< 10^8-7\Rightarrow\frac{1}{10^7-8}>\frac{1}{10^8-7}\Rightarrow\frac{13}{10^7-8}>\frac{13}{10^8-7}\Rightarrow A>B\)

c,Áp dụng nếu \(\frac{a}{b}>1\Rightarrow\frac{a}{b}>\frac{a+n}{a+n}\) có:

 \(B=\frac{10^{1993}+1}{10^{1992}+1}>\frac{10^{1993}+1+9}{10^{1992}+1+9}=\frac{10^{1993}+10}{10^{1992}+10}=\frac{10\left(10^{1992}+1\right)}{10\left(10^{1991}+1\right)}=\frac{10^{1992}+1}{10^{1991}+1}=A\)

Vậy A < B

Có :

A = 10 - 9/10^1991+1

B = 10 - 9/10^1992+1

Vì 10^1991+1 < 10^1992+1 => 9/10^1991+1 > 9/10^1992+1

=> A < B

Tk mk nha

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

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

b: \(A=\dfrac{10^7-8+13}{10^7-8}=1+\dfrac{13}{10^7-8}\)

\(B=\dfrac{10^8-7+13}{10^8-7}=1+\dfrac{13}{10^8-7}\)

mà \(10^7-8< 10^8-7\)

nên A>B

c: \(\dfrac{1}{10}A=\dfrac{10^{1992}+1}{10^{1992}+10}=1-\dfrac{9}{10^{1992}+10}\)

\(\dfrac{1}{10}B=\dfrac{10^{1993}+1}{10^{1993}+10}=1-\dfrac{9}{10^{1993}+10}\)

mà \(\dfrac{9}{10^{1992}+10}>\dfrac{9}{10^{1993}+10}\)

nên A<B

\(\frac{A}{10}=\frac{10^{1992}+1}{10^{1992}+10}=\frac{\left(10^{1992}+10\right)-9}{10^{1992}+10}=1-\frac{9}{10^{1992}+10}\)

\(\frac{B}{10}=\frac{10^{1993}+1}{10^{1993}+10}=\frac{\left(10^{1993}+10\right)-9}{10^{1993}+10}=1-\frac{9}{10^{1993}+10}\)

Vì \(10^{1992}+10< 10^{1993}+10\) nên \(1+\frac{9}{10^{1993}+10}>1+\frac{9}{10^{1993}+10}\)

Do đó \(A>B\)

lấy máy tính mà tính!

tất nhiên A>B

Áp dụng tính chất \(\dfrac{a}{b}< 1\Rightarrow\dfrac{a}{b}< \dfrac{a+m}{b+m}\) ta có:

\(A=\dfrac{10^{1992}+1}{10^{1993}+1}< \dfrac{10^{1992}+1+9}{10^{1993}+1+9}=\dfrac{10^{1992}+10}{10^{1993}+10}\)

\(=\dfrac{10\left(10^{1991}+1\right)}{10\left(10^{1992}+1\right)}=\dfrac{10^{1991}+1}{10^{1992}+1}\)

\(\Rightarrow\dfrac{10^{1992}+1}{10^{1993}+1}< \dfrac{10^{1991}+1}{10^{1992}+1}\)

Hay \(A>B\)

Ta đi so sánh:

\(\dfrac{1}{A}=\dfrac{10^{1991}+1}{10^{1992}+1}\) và \(\dfrac{1}{B}=\dfrac{10^{1992}+1}{10^{1993}+1}\)

Ta có:\(\dfrac{10}{A}=\dfrac{10^{1992}+10}{10^{1992}+1}\)

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

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

\(\dfrac{10}{B}=\dfrac{10^{1993}+10}{10^{1993}+1}\)

\(=\dfrac{10^{1993}+1+9}{10^{1993}+11}\)

Mà \(\dfrac{9}{10^{1992}+1}>\dfrac{9}{10^{1993}+1}\)

\(\Rightarrow\dfrac{10}{A}>\dfrac{10}{B}\)

Vậy A<B

\(\dfrac{\cosh}{ }\)

Ta viết lại A như sau:

\(A=\frac{10^{1992}+1}{10^{1991}+1}\)

\(=\frac{10^{1991}X10+1}{10^{1991}+1}\)

\(=\frac{10+1}{1}\)

\(=\frac{11}{1}\)

\(=11\)