Question

x+24/1996 + x+25/1995 + x+26/1994 + x+2036/4=0

Answer 1

\(\dfrac{x+24}{1996}+\dfrac{x+25}{1995}+\dfrac{x+26}{1994}+\dfrac{x+2036}{4}=0\\ \Leftrightarrow\left(\dfrac{x+24}{1996}+1\right)+\left(\dfrac{x+25}{1995}+1\right)+\left(\dfrac{x+26}{1994}+1\right)+\left(\dfrac{x+2036}{4}-3\right)=0\\ \Leftrightarrow\dfrac{x+2020}{1996}+\dfrac{x+2020}{1995}+\dfrac{x+2020}{1994}+\dfrac{x+2020}{4}=0\\ \Leftrightarrow\left(x+2020\right)\left(\dfrac{1}{1996}+\dfrac{1}{1995}+\dfrac{1}{1994}+\dfrac{1}{4}\right)=0\\ \Leftrightarrow x+2020=0\\ \Leftrightarrow x=-2020\)