\(\frac{19^{30}+5}{19^{31}+5}\)và \(\frac{19^{31}+5}{19^{32}+5}\)

Xét biểu thức \(\frac{19^{30}+5}{19^{31}+5}\)là A và biểu thức \(\frac{19^{31}+5}{19^{32}+5}\)là B

\(B=\frac{19^{31}+5}{19^{32}+5}< \frac{19^{31}+5+14}{19^{32}+5+14}\)

\(=\)\(\frac{19^{31}.19}{19^{32}.19}\)\(=\)\(\frac{19.\left(19^{30}+1\right)}{19.\left(19^{31}+1\right)}\)

\(=\)\(\frac{19^{30}+1}{19^{31}+1}\)

Mà \(\frac{19^{30}+1}{19^{31}+1}< \frac{19^{30}+5}{19^{31}+5}\)

Nên \(A>B\)

Xét B = \(\frac{19^{31}+5}{19^{32}+5}< \frac{19^{31}+5+14}{19^{32}+5+14}=\frac{19^{31}.19}{19^{32}.19}=\frac{19\left(19^{30}+1\right)}{19\left(19^{31}+1\right)}=\frac{19^{30}+1}{19^{31}+1}< \frac{19^{30}+5}{19^{31}+5}=A\)Vậy A > B

Xét B = \(\frac{19^{31}+5}{19^{32}+5}< \frac{19^{31}+19}{19^{32}+19}=\frac{19\left(19^{30}+1\right)}{19\left(19^{31}+1\right)}=\frac{19^{30}+1}{19^{31}+1}< \frac{19^{30}+5}{19^{31}+5}=A\)

Vậy A > B

Ta có: \(A=\frac{19^{30}+5}{19^{31}+5}\Rightarrow19A=\frac{19.\left(19^{30}+5\right)}{19^{31}+5}=\frac{19^{31}+95}{19^{31}+5}=\frac{19^{31}+5+90}{19^{31}+5}=1+\frac{90}{19^{31}+5}\)

    \(B=\frac{19^{31}+5}{19^{32}+5}\Rightarrow19B=\frac{19.\left(19^{31}+5\right)}{19^{32}+5}=\frac{19^{32}+95}{19^{32}+5}=\frac{19^{32}+5+90}{19^{32}+5}=1+\frac{90}{19^{32}+5}\)

Nên  \(19A< 19B\Rightarrow A< B\)

Nhầm: Vì \(\frac{90}{19^{31}+5}>\frac{90}{19^{32}+5}\Rightarrow1+\frac{90}{19^{31}+5}>1+\frac{90}{19^{32}+5}\Rightarrow A>B\)

= nhau

mk chắc chắn cần gải ra bảo mk 

:3

\(19A=\frac{19^{31}+95}{19^{31}+5}=1+\frac{90}{19^{31}+5}\)

\(19B=\frac{19^{32}+95}{19^{32}+5}=1+\frac{90}{19^{32}+5}\)

Ta thấy \(19A>19B\) nên A > B

Ta có \(A=\frac{19^{30}+5}{19^{31}+5}\)

Suy ra \(19A=\frac{19^{31}+95}{19^{31}+5}=\frac{19^{31}+5}{19^{31}+5}+\frac{90}{19^{31}+5}=1+\frac{90}{19^{31}+5}\)

Ta có \(B=\frac{19^{31}+5}{19^{32}+5}\)

Suy ra  \(19B=\frac{19^{32}+95}{19^{32}+5}=\frac{19^{32}+5}{19^{32}+5}+\frac{90}{19^{32}+5}=1+\frac{90}{19^{32}+5}\)

Vì \(19^{31}+5< 19^{32}+5\Rightarrow\frac{90}{19^{31}+5}>\frac{90}{19^{32}+5}\Rightarrow1+\frac{90}{19^{31}+5}>1+\frac{90}{19^{32}+5}\)

Do đó \(19A>19B\Rightarrow A>B\)

Vậy A > B

\(19A=\frac{19\left(19^{30}+5\right)}{19^{31}+5}=\frac{19^{31}+95}{19^{31}+5}=1+\frac{90}{19^{31}+5}\)

\(19B=\frac{19\left(19^{31}+5\right)}{19^{32}+5}=\frac{19^{32}+95}{19^{32}+5}=1+\frac{90}{19^{32}+5}\)

Do \(\frac{90}{19^{31}+5}>\frac{90}{19^{32}+5}\)

Nên \(1+\frac{90}{19^{31}+5}>1+\frac{90}{19^{32}+5}\)

Hay 19A>19B 

Suy ra A>B 

Vậy A>B