\(\frac{2020}{2019}-\frac{2018}{2017}+\frac{2}{2017\cdot2019}3\cdot x-18\)
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TS
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19 tháng 6 2017
Ta có : \(\frac{x-1}{2017}+\frac{x-2}{2018}-\frac{x-3}{2019}=\frac{x-4}{2020}\)
\(\Rightarrow\frac{x-1}{2017}+\frac{x-2}{2018}=\frac{x-4}{2020}+\frac{x-3}{2019}\)
\(\Rightarrow1+\frac{x-1}{2017}+1+\frac{x-2}{2018}=1+\frac{x-4}{2020}+1+\frac{x-3}{2019}\)
\(\Rightarrow\frac{2016+x}{2017}+\frac{2016+x}{2018}=\frac{2016+x}{2020}+\frac{2016+x}{2019}\)
\(\Rightarrow\frac{2016+x}{2017}+\frac{2016+x}{2018}-\frac{2016+x}{2019}-\frac{2016+x}{2020}=0\)
\(\Rightarrow\left(2016+x\right)\left(\frac{1}{2017}+\frac{1}{2018}-\frac{1}{2019}-\frac{1}{2020}\right)=0\)
\(\text{Mà :
}\)\(\frac{1}{2017}+\frac{1}{2018}-\frac{1}{2019}-\frac{1}{2020}\ne0\)
\(\text{Nên : }\) \(2016+x=0\)
\(\Rightarrow x=-2016\)
16 tháng 4 2020
Ta có:\(\frac{x-2}{2017}+1+\frac{x-3}{2018}+1=\frac{x-4}{2019}+1+\frac{x-5}{2020}+1\)
\(\Rightarrow\frac{x+2015}{2017}+\frac{x+2015}{2018}-\frac{x+2015}{2019}-\frac{x+2015}{2020}=0\)
\(\Rightarrow\left(x+2015\right)\left(\frac{1}{2017}+\frac{1}{2018}-\frac{1}{2019}-\frac{1}{2020}\right)=0\)
Mà \(\frac{1}{2017}+\frac{1}{2018}-\frac{1}{2019}-\frac{1}{2020}>0\)
\(\Rightarrow x+2015=0\Rightarrow x=-2015\)
\(S=\left\{-2015\right\}\)
DL
17 tháng 6 2019
Ta đi so sánh \(\frac{2017.2018+1}{2017.2018}\)với\(\frac{2018.2019+1}{2018.2019}\)có :
\(\frac{2017.2018+1}{2017.2018}=\frac{2017.2018}{2017.2018}+\frac{1}{2017.2018}=1+\frac{1}{2017.2018}\left(\cdot\right)\)
\(\frac{2018.2019+1}{2018.2019}=\frac{2018.2019}{2018.2019}+\frac{1}{2018.2019}\left(\cdot\cdot\right)\)
\(\frac{1}{2017.2018}>\frac{1}{2018.2019}\left(\cdot\cdot\cdot\right)\)Từ \(\left(\cdot\right);\left(\cdot\cdot\right)\&\left(\cdot\cdot\cdot\right)\Rightarrow\frac{2017.2018+1}{2017.2018}>\frac{2018.2019+1}{2018.2019}\)
\(\Leftrightarrow\frac{2017.2018}{2017.2018+1}< \frac{2018.2019}{2018.2019+1}.\)
24 tháng 7 2018
\(A=\frac{2017.2018-1}{2017.2018}=1-\frac{1}{2017.2018}\)
\(B=\frac{2018.2019-1}{2018.2019}=1-\frac{1}{2018.2019}\)
Có \(\frac{1}{2017.2018}>\frac{1}{2018.2019}\)
\(\Rightarrow A< B\)
8 tháng 8 2017
\(\frac{19}{37}+\left(1-\frac{19}{37}\right)\)
\(=\frac{19}{37}+1-\frac{19}{37}\)
\(=\left(\frac{19}{37}-\frac{19}{37}\right)+1\)
\(=0+1=1\)
Đề là gì vậy bạn !