so sánh hai phân số A=2021^5+7/2021^5-1 và B=2021^9+5/2021^9-3 17/10/2021 Bởi Isabelle so sánh hai phân số A=2021^5+7/2021^5-1 và B=2021^9+5/2021^9-3
$A=\dfrac{2021^5+7}{2021^5-1}\\ =\dfrac{2021^5-1+8}{2021^5-1}\\ =1+\dfrac{8}{2021^5-1}\\ B=\dfrac{2021^9+5}{2021^9-3}\\ =\dfrac{2021^9-3+8}{2021^9-3}\\ =1+\dfrac{8}{2021^9-3}\\ 2021^9-3>2021^5-1(2021^9=2021^4.2021^5>2.2021^5=2021^5+2021^5>2021^5+3-1)\\ \Rightarrow \dfrac{8}{2021^9-3}<\dfrac{8}{2021^5-1}\\ \Rightarrow B<A$ Bình luận
`A=(2021^5+1)/(2021^5-1)=1+8/(2021^5-1)` `B=(2021^9+5)/(2021^9-3)=1+8/(2021^9-3)` Mà `2021^9-3>2021^5-1` `=>A>B` Bình luận
$A=\dfrac{2021^5+7}{2021^5-1}\\ =\dfrac{2021^5-1+8}{2021^5-1}\\ =1+\dfrac{8}{2021^5-1}\\ B=\dfrac{2021^9+5}{2021^9-3}\\ =\dfrac{2021^9-3+8}{2021^9-3}\\ =1+\dfrac{8}{2021^9-3}\\ 2021^9-3>2021^5-1(2021^9=2021^4.2021^5>2.2021^5=2021^5+2021^5>2021^5+3-1)\\ \Rightarrow \dfrac{8}{2021^9-3}<\dfrac{8}{2021^5-1}\\ \Rightarrow B<A$
`A=(2021^5+1)/(2021^5-1)=1+8/(2021^5-1)`
`B=(2021^9+5)/(2021^9-3)=1+8/(2021^9-3)`
Mà `2021^9-3>2021^5-1`
`=>A>B`