So sánh A=2017^2017+1/2017^2018+1 và B=2017^2016+1/2017^2017+1
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: 58/63=3190/3465
36/55=2268/3465
=>58/63>36/55
b: 27/53=1998/3922
36/74=1908/3922
=>27/53>36/74
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Bn quy đồng rồi làm nha
b,Có A=2017^2017+1/2017^2018+1
--> 2017A=2017^2018+2017/2017^2018+1
2017A=2017^2018+1/2017^2018+1 + 2016/2017^2018+1
2017A=1+ 2016/2017^2018+1
Có B=2017^2016+1/2017^2017+1
--> 2017B=2017^2017+2017/2017^2017+1
2017B=2017^2017+1/2017^2017+1 + 2016/2017^2017+1
2017B=1+2016/2017^2017+1
Vì 1+2016/2017^2018+1 < 1+2016/2017^2017+1
nên 2017A<2017B
-->A<B
A.Ta có :
\(A=-\frac{15}{46}>-\frac{15}{45}=-\frac{51}{153}>-\frac{51}{151}=B\)
\(\Rightarrow A>B\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Tính A và B rồi ta đi so sánh:
A = \(\frac{2016}{2017}\) + \(\frac{2017}{2018}\) = \(1.999008674\)
B = \(\frac{2016+2017}{2017+2018}\) = \(0.9995043371\)
Mà 1.999008674 > 0.9995043371
Nên: A > B
Vi \(\frac{2017^{2017}+1}{2017^{2018}+1}< 1\)
\(\Rightarrow A=\frac{2017^{2017}+1}{2017^{2018}+1}< \frac{2017^{2017}+1+2016}{2017^{2018}+1+2016}=\frac{2017^{2017}+2017}{2017^{2018}+2017}=\frac{2017\left(2017^{2016}+1\right)}{2017\left(2017^{2017}+1\right)}=\frac{2017^{2016}+1}{2017^{2017}+1}=B\)Vay A < B