Question

So sánh : A với B

 

A=5^5+2/5^5-1

B=5^5/5^5-3

Answer 1

Ta có : 

\(A=\frac{5^5+2}{5^5-1}=\frac{5^5-1}{5^5-1}+\frac{3}{5^5-1}\)

                 \(=1+\frac{3}{5^5-1}\)

\(B=\frac{5^5}{5^5-3}=\frac{5^5-3}{5^5-3}+\frac{3}{5^5-3}\)

                  \(=1+\frac{3}{5^5-3}\)

\(5^5-1>5^5-3\)

\(\Rightarrow\frac{3}{5^5-1}< \frac{3}{5^5-3}\)

\(\Rightarrow1+\frac{3}{3^5-1}< 1+\frac{3}{3^5-3}\)

\(\Rightarrow A>B\)

Vậy \(A>B\)