\(\dfrac{x+30}{2007}+\dfrac{x+32}{2005}=\dfrac{x+34}{2003}+\dfrac{x+36}{2001}\)
\(\Leftrightarrow\dfrac{x+30}{2007}+1+\dfrac{x+32}{2005}+1=\dfrac{x+34}{2003}+1+\dfrac{x+36}{2001}+1\)
\(\Leftrightarrow\dfrac{x+2037}{2007}+\dfrac{x+2037}{2005}=\dfrac{x+2037}{2003}+\dfrac{x+2037}{2001}\)
\(\Leftrightarrow\dfrac{x+2037}{2007}+\dfrac{x+2037}{2005}-\dfrac{x+2037}{2003}-\dfrac{x+2037}{2001}=0\)
\(\Leftrightarrow\left(x+2037\right)\left(\dfrac{1}{2007}+\dfrac{1}{2005}-\dfrac{1}{2003}-\dfrac{1}{2001}\right)=0\)
\(\Rightarrow x+2037=0\).Do \(\dfrac{1}{2007}+\dfrac{1}{2005}-\dfrac{1}{2003}-\dfrac{1}{2001}\ne0\)
\(\Rightarrow x=-2037\)
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Bài làm
\(\dfrac{x+30}{2007}+\dfrac{x+32}{2005}=\dfrac{x+34}{2003}+\dfrac{x+36}{2001}\)
\(\dfrac{x+30}{2007}+\dfrac{x+32}{2005}-\dfrac{x+34}{2003}-\dfrac{x+36}{2001}=0\)
\(\left(\dfrac{x+30}{2007}+1\right)+\left(\dfrac{x+32}{2005}+1\right)-\left(\dfrac{x+34}{2003}+1\right)-\left(\dfrac{x+36}{2001}+1\right)=0\)
\(\dfrac{x+30+2007}{2007}+\dfrac{x+32+2005}{2005}-\dfrac{x+34+2003}{2003}-\dfrac{x+36+2001}{2001}=0\)\(\dfrac{x+2037}{2007}+\dfrac{x+2037}{2005}-\dfrac{x+2037}{2003}-\dfrac{x+2037}{2001}=0\)\(\left(x+2037\right).\left(\dfrac{1}{2007}+\dfrac{1}{2005}-\dfrac{1}{2003}-\dfrac{1}{2001}\right)=0\)
x+2037=0
x = -2037