\(\Leftrightarrow\left(\frac{x+1}{2009}+1\right)\left(\frac{x+2}{2008}+1\right)\left(\frac{x+17}{1993}+1\right)=0\) 0
\(\Leftrightarrow\frac{x+2020}{2009}\cdot\frac{x+2020}{2008}\cdot\frac{x+2020}{1993}=0\)
\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{1993}\right)=0\)
\(\Rightarrow x+2020=0\)(do \(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{1993}\ne0\)
\(\Leftrightarrow x=2020\)
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