Question

So sánh

\(A=\frac{115^{17}+2}{115^{17}-1}\)

\(B=\frac{115^{17}}{115^{17}-3}\)

Answer 1

\(A=\frac{115^{17}+2}{115^{17}-1}=\frac{115^{17}}{115^{17}-\left(2+1\right)}=\frac{115^{17}}{115^{17}-3}\)

\(\Rightarrow A=B\)

Answer 2

Ta có :

A = \(\frac{115^{17}+2}{115^{17}-1}\)= \(\frac{115^{17}-1+3}{115^{17}-1}\)= 1 + \(\frac{3}{115^{17}-1}\)

B = \(\frac{115^{17}}{115^{17}-3}\)= \(\frac{115^{17}-3+3}{115^{17}-3}\)= 1 + \(\frac{3}{115^{17}-3}\)

Vì 115¹⁷ - 1 > 115¹⁷ - 3 nên  \(\frac{3}{115^{17}-3}\) <  \(\frac{3}{115^{17}-1}\)

Vậy :1 + \(\frac{3}{115^{17}-1}\) < 1 + \(\frac{3}{115^{17}-3}\) hay A < B