\(\frac{x-15}{2014}+\frac{x-20}{2019}=\frac{x-5}{2004}+\frac{x+30}{1969}\)
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OM
5 tháng 4 2020
a, Làm
\(\frac{x+1}{2020}+\frac{x+2}{2019}+\frac{x+3}{2018}=\frac{x+4}{2017}+\frac{x+5}{2016}+\frac{x+6}{2015}\)
<=>\(\frac{x+2021}{2020}+\frac{x+2021}{2019}+\frac{x+2021}{2018}=\frac{x+2021}{2017}+\frac{x+2021}{2016}+\frac{x+2021}{2015}\)
<=>\(\left(x+2021\right)\left(\frac{1}{2020}+\frac{1}{2019}+\frac{1}{2018}-\frac{1}{2017}-\frac{1}{2016}-\frac{1}{2015}\right)=0\)
<=> x+2021=0
<=> x=-2021
Kl:......................
b, Làmmmmm
\(\frac{2-x}{2004}-1=\frac{1-x}{2005}-\frac{x}{2006}\)
<=> \(\frac{2006-x}{2004}=\frac{2006-x}{2005}+\frac{2006-x}{2006}\)
<=> \(\left(2006-x\right)\left(\frac{1}{2004}-\frac{1}{2005}-\frac{1}{2006}\right)=0< =>2006-x=0\)
<=> x=2006
Kl:..............
25 tháng 2 2019
\(\frac{x+5}{95}+\frac{x+3}{97}+\frac{x+1}{99}=\frac{x+15}{85}+\frac{x+20}{80}+\frac{x+25}{75}.\)
\(\frac{x+5}{95}+1+\frac{x+3}{97}+1+\frac{x+1}{99}+1-\frac{x+15}{85}-1-\frac{x+20}{80}-1-\frac{x+25}{75}-1=0\)
\(\frac{x+100}{95}+\frac{x+100}{97}+\frac{x+100}{99}-\frac{x+100}{85}-\frac{x+100}{80}-\frac{x+100}{75}=0\)
\(\left(x+100\right).\left(\frac{1}{95}+\frac{1}{97}+\frac{1}{99}-\frac{1}{85}-\frac{1}{80}-\frac{1}{75}\right)=0\)
\(\Rightarrow x+100=0\Rightarrow x=-100\)
\(\frac{1}{95}+\frac{1}{97}+\frac{1}{99}-\frac{1}{85}-\frac{1}{80}-\frac{1}{75}\ne0\)
TT
7 tháng 3 2020
Gợi ý :
Bài 1 : Cộng thêm 1 vào 3 phân thức đầu, trừ cho 3 ở phân thức thứ 4, có nhân tử chung là (x+2020)
Bài 2 : Trừ mỗi phân thức cho 1, chuyển vế và có nhân tử chung là (x-2021)
Bài 3 : Phân thức thứ nhất trừ đi 1, phân thức hai trù đi 2, phân thức ba trừ đi 3, phân thức bốn trừ cho 4, phân thức 5 trừ cho 5. Có nhân tử chung là (x-100)
I
7 tháng 3 2020
bài 3
\(\frac{x-90}{10}+\frac{x-76}{12}+\frac{x-58}{14}+\frac{x-36}{16}+\frac{x-15}{17}=15.\)
=>\(\frac{x-90}{10}-1+\frac{x-76}{12}-2+\frac{x-58}{14}-3+\frac{x-36}{16}-4+\frac{x-15}{17}-5=0\)
=>\(\frac{x-100}{10}+\frac{x-100}{12}+\frac{x-100}{14}+\frac{x-100}{16}+\frac{x-100}{17}=0\)
=>\(\left(x-100\right).\left(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\right)=0\)
=>(x-100)=0 do \(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\ne0\)
=> x=100
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 \(\frac{1}{2017}+\frac{1}{2018}-\frac{1}{2019}-\frac{1}{2020}>0\)
\(\Rightarrow x+2015=0\Rightarrow x=-2015\)
\(S=\left\{-2015\right\}\)
NN
13 tháng 11 2020
\(\frac{x+1}{2008}+\frac{x+2}{2007}+\frac{x+3}{2006}=\frac{x+4}{2005}+\frac{x+5}{2004}+\frac{x+6}{2003}\)
\(\Leftrightarrow\frac{x+1}{2008}+\frac{x+2}{2007}+\frac{x+3}{2006}+3=\frac{x+4}{2005}+\frac{x+5}{2004}+\frac{x+6}{2003}+3\)
\(\Leftrightarrow\left(\frac{x+1}{2008}+1\right)+\left(\frac{x+2}{2007}+1\right)+\left(\frac{x+3}{2006}+1\right)=\left(\frac{x+4}{2005}+1\right)\)
\(+\left(\frac{x+5}{2004}+1\right)+\left(\frac{x+6}{2003}+1\right)\)
\(\Leftrightarrow\frac{x+2009}{2008}+\frac{x+2009}{2007}+\frac{x+2009}{2006}=\frac{x+2009}{2005}+\frac{x+2009}{2004}+\frac{x+2009}{2003}\)
\(\Leftrightarrow\frac{x+2009}{2008}+\frac{x+2009}{2007}+\frac{x+2009}{2006}-\frac{x+2009}{2005}-\frac{x+2009}{2004}-\frac{x+2009}{2003}=0\)
\(\Leftrightarrow\left(x+2009\right)\left(\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\right)=0\)(1)
Vì \(\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\ne0\)(2)
Từ (1) và (2) \(\Rightarrow x+2009=0\)\(\Rightarrow x=-2009\)
Vậy \(x=-2009\)
KY
1
M
10 tháng 1 2016
Ta có : \(\frac{x+5}{2006}+\frac{x+6}{2005}+\frac{x+7}{2004}=-3\)
=> \(\left(\frac{x+5}{2006}+1\right)+\left(\frac{x+6}{2005}+1\right)+\left(\frac{x+7}{2004}+1\right)=-3+3\)
=> \(\frac{x+5+2006}{2006}+\frac{x+6+2005}{2005}+\frac{x+7+2004}{2004}=0\)
=> \(\frac{x+2011}{2006}+\frac{x+2011}{2005}+\frac{x+2011}{2004}=0\)
=> \(\left(x+2011\right)\left(\frac{1}{2006}+\frac{1}{2005}+\frac{1}{2004}\right)=0\)
Ta có : \(\frac{1}{2006}+\frac{1}{2005}+\frac{1}{2004}\ne0\)
=> x + 2011 = 0
=> x = -2011
\(\frac{x-15}{2014}+\frac{x-20}{2019}=\frac{x-5}{2004}+\frac{x+30}{1969}\)
\(\Leftrightarrow\frac{x-15}{2014}+1+\frac{x-20}{2019}+1=\frac{x-5}{2004}+1+\frac{x+30}{1969}+1\)
\(\Leftrightarrow\frac{x-15+2014}{2014}+\frac{x-20+2019}{2019}-\frac{x-5+2004}{2004}-\frac{x+30+1969}{1969}=0\)
\(\Leftrightarrow\frac{x-1999}{2014}+\frac{x+1999}{2019}-\frac{x+1999}{2004}-\frac{x+1999}{1969}=0\)
\(\Leftrightarrow\left(x-1999\right)\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)=0\)
Vì \(\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)\ne0\)
nên \(x-1999=0\)
\(\Leftrightarrow x=1999\)
\(easy!\)(sai đề + sửa đề)
\(\frac{x-5}{2014}+\frac{x-20}{2019}-\frac{x-5}{2004}-\frac{x+3}{1969}=0\)
\(\Leftrightarrow\left(\frac{x-15}{2014}-1\right)+\left(\frac{x-20}{2019}-1\right)-\left(\frac{x-5}{2004}-1\right)-\left(\frac{x-30}{1969}-1\right)=0\)
\(\Leftrightarrow\frac{x-1999}{2014}+\frac{x-1999}{2019}-\frac{x-1999}{2004}-\frac{x-1999}{1969}=0\)
\(\Leftrightarrow\left(x-1999\right)\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)=0\)
dễ dàng cm được \(x-1999=0\)
\(\Leftrightarrow x=1999\)