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\(\frac{x+5}{2005}+\frac{x+6}{2004}+\frac{x+7}{2003}=-3\)
\(\Leftrightarrow\frac{x+5}{2005}+1+\frac{x+6}{2004}+1+\frac{x+7}{2003}+1=0\)
\(\Leftrightarrow\frac{x+2010}{2005}+\frac{x+2010}{2004}+\frac{x+2010}{2003}=0\)
\(\Leftrightarrow x+2010=0\)
\(\Leftrightarrow x=-2010\).
Ta có :
\(\frac{x+3}{2003}+\frac{x+2}{2004}+\frac{x+1}{2005}=-3\)
\(\Leftrightarrow\)\(\left(\frac{x+3}{2003}+1\right)\left(\frac{x+2}{2004}+1\right)\left(\frac{x+1}{2005}+1\right)=-3+3\)
\(\Leftrightarrow\)\(\frac{x+2006}{2003}+\frac{x+2006}{2004}+\frac{x+2006}{2005}=0\)
\(\Leftrightarrow\)\(\left(x+2006\right)\left(\frac{1}{2003}+\frac{1}{2004}+\frac{1}{2005}\right)=0\)
Vì \(\frac{1}{2003}+\frac{1}{2004}+\frac{1}{2005}\ne0\)
Nên \(x+2006=0\)
\(\Rightarrow\)\(x=-2006\)
Vậy \(x=-2006\)
Chúc bạn học tốt ~
\(\frac{x-1}{2005}+\frac{x-2}{2004}-\frac{x-3}{2003}=\frac{x-4}{2002}\)
=>\(\frac{x-1}{2005}+\frac{x-2}{2004}-\frac{x-3}{2003}-\frac{x-4}{2004}=0\)
=>\(\left(\frac{x-1}{2005}-1\right)+\left(\frac{x-2}{2004}-1\right)-\left(\frac{x-3}{2003}-1\right)-\left(\frac{x-4}{2002}-1\right)=0\)
=>\(\frac{x-1-2005}{2005}+\frac{x-2-2004}{2004}-\frac{x-3-2003}{2003}-\frac{x-4-2002}{2002}=0\)
=>\(\frac{x-2006}{2005}+\frac{x-2006}{2004}-\frac{x-2006}{2003}-\frac{x-2006}{2002}=0\)
=>\(\left(x-2006\right)\left(\frac{1}{2005}+\frac{1}{2004}-\frac{1}{2003}-\frac{1}{2002}\right)=0\)
Mà \(\frac{1}{2005}+\frac{1}{2004}-\frac{1}{2003}-\frac{1}{2002}\ne0\)
=> x - 2006 = 0 => x = 2006