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Đề đúng phải là:
\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}=\frac{x+10}{2005}+\frac{x+11}{2004}+\frac{x+12}{2003}\)
Cộng mỗi phân thức thêm 1, quy đồng rồi chuyển sang 1 vế ta được:
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}-\frac{x+2015}{2005}-\frac{x+2015}{2004}-\frac{x+2015}{2003}=0\)
\(\Leftrightarrow\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\right)=0\)
Mà BT tích sau luôn nhỏ hơn 0
=> x+2015=0 => x = -2015
\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}=\frac{x+10}{2005}+\frac{x+11}{2004}+\frac{x+12}{2003}\)( như này đúng không ? :)) )
<=> \(\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)+\left(\frac{x+3}{2012}+1\right)=\left(\frac{x+10}{2005}+1\right)+\left(\frac{x+11}{2004}+1\right)+\left(\frac{x+12}{2003}+1\right)\)
<=> \(\frac{x+1+2014}{2014}+\frac{x+2+2013}{2013}+\frac{x+3+2012}{2012}=\frac{x+10+2005}{2005}+\frac{x+11+2004}{2004}+\frac{x+12+2003}{2003}\)
<=> \(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=\frac{x+2015}{2005}+\frac{x+2015}{2004}+\frac{x+12}{2003}\)
<=> \(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}-\frac{x+2015}{2005}-\frac{x+2015}{2004}-\frac{x+12}{2003}=0\)
<=> \(\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\right)=0\)
Vì \(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\ne0\)
=> x + 2015 = 0
=> x = -2015
a) (x-5)x+2015 - (x-5)x+2014 =0
(x-5)x+2014(x-5 -1) =0
+ x -5 =0 => x =5
+ x -6 =0 => x =6
Vậy x = 5 hoặc x =6
\(\frac{x-1}{2005}+\frac{x-2}{2004}-\frac{x-3}{2003}=\frac{x-4}{2002}\)
=>\(\frac{x-1}{2005}+\frac{x-2}{2004}-\frac{x-3}{2003}-\frac{x-4}{2004}=0\)
=>\(\left(\frac{x-1}{2005}-1\right)+\left(\frac{x-2}{2004}-1\right)-\left(\frac{x-3}{2003}-1\right)-\left(\frac{x-4}{2002}-1\right)=0\)
=>\(\frac{x-1-2005}{2005}+\frac{x-2-2004}{2004}-\frac{x-3-2003}{2003}-\frac{x-4-2002}{2002}=0\)
=>\(\frac{x-2006}{2005}+\frac{x-2006}{2004}-\frac{x-2006}{2003}-\frac{x-2006}{2002}=0\)
=>\(\left(x-2006\right)\left(\frac{1}{2005}+\frac{1}{2004}-\frac{1}{2003}-\frac{1}{2002}\right)=0\)
Mà \(\frac{1}{2005}+\frac{1}{2004}-\frac{1}{2003}-\frac{1}{2002}\ne0\)
=> x - 2006 = 0 => x = 2006
\(\frac{x+5}{2005}+1+\frac{x+6}{2004}+1+\frac{x+7}{2003}+1=0\)
<=> \(\frac{x+2010}{2005}+\frac{x+2010}{2004}+\frac{x+2010}{2003}=0\)
<=>\(\left(x+2010\right)\left(\frac{1}{2005}+\frac{1}{2004}+\frac{1}{2003}\right)=0\)
<=>x+2010=0
<=>x=-2010
\(\frac{x+2005}{2004}-\frac{x+2005}{2001}=\frac{x+2005}{2002}-\frac{x+2005}{2003}\)
\(\frac{x+2005}{2004}-\frac{x+2005}{2001}+\frac{x+2005}{2003}-\frac{x+2005}{2002}=0\)
\(\left(x+2005\right).\left(\frac{1}{2004}-\frac{1}{2001}+\frac{1}{2003}-\frac{1}{2002}\right)=0\)
=> x + 2015 = 0
=> x = -2015
Vậy x = -2015
TL :
\(\frac{x+2005}{2004}-\frac{x+2005}{2001}=\frac{x+2005}{2002}-\frac{x+2005}{2003}\)
\(\frac{x+2005}{2004}-\frac{x+2005}{2001}+\frac{x+2005}{2002}-\frac{x+2005}{2003}=0\)
Ta có : \(\left(x+2005\right).\left(\frac{1}{2004}-\frac{1}{2001}+\frac{1}{2003}-\frac{1}{2002}\right)=0\)
\(\Rightarrow x+2005=0\)
\(\Rightarrow x=-2005\)
\(\frac{x+5}{2005}+\frac{x+6}{2004}+\frac{x+7}{2003}=-3\)
\(\frac{x+5}{2005}+\frac{x+6}{2004}+\frac{x+7}{2003}+3=0\)
\(\left(\frac{x+5}{2005}+1\right)+\left(\frac{x+6}{2004}+1\right)+\left(\frac{x+7}{2003}+1\right)=0\)
\(\frac{x+5+2005}{2005}+\frac{x+6+2004}{2004}+\frac{x+7+2003}{2003}=0\)
\(\frac{x+2010}{2005}+\frac{x+2010}{2004}+\frac{x+2012}{2003}=0\)
\(\left(x+2010\right)\left(\frac{1}{2005}+\frac{1}{2006}+\frac{1}{2007}\right)=0\)
\(x+2010=0\)
\(x=-2010\)
\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(\Rightarrow\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=0\)
\(\Rightarrow\frac{x+1+1974}{1974}+\frac{x+2+1973}{1973}+\frac{x+3+1972}{1972}=0\)
\(\Rightarrow\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\Rightarrow\left(x+1975\right)\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}=0\)
Mà \(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\ne0\)
\(\Rightarrow x+1975=0\)
\(\Rightarrow x=0+1975\)
\(\Rightarrow x=1975\)
Vậy \(x=1975\)
b) phần này làm tương tự phần a nha, chuyển -3 sang vế bên trái r cộng từng p.số vs 1 và sau đó nhóm tử số chung ra ngoài ^^
