[tex] \frac{x+1}{2}+ \frac{x+2}{3}+ \frac{x+3}{4}+...+ \frac{x+99}{100}=99\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ (\frac{x+1}{2}-1) +(\frac{x+2}{3}-1)+ (\frac{x+3}{4}-1) +...+ (\frac{x+99}{100}-1)=0 \ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ \frac{x-1}{2}+ \frac{x-1}{3}+ \frac{x-1}{4}+ ...+\frac{x-1}{100} =0\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ (x-1)( \frac{1}{2}+ \frac{1}{3}+ \frac{1}{4} +. ..+\frac{1}{100} )=0=\ \textgreater \ (x-1)=0=\ \textgreater \ \boxed{x=1}. \\ \\ Solutie:~x=1.[/tex]
