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\(\cfrac{x+1}{2}+\cfrac{2}{x+1}=\cfrac{x+1}{3}+\cfrac{3}{x+1}-\cfrac{5}{6}\)
বা, \(\cfrac{x+1}{2}+\cfrac{2}{x+1}-\cfrac{x+1}{3}-\cfrac{3}{x+1}=-\cfrac{5}{6}\)
বা, \(\cfrac{x+1}{2}-\cfrac{x+1}{3}+\cfrac{2}{x+1}-\cfrac{3}{x+1}=-\cfrac{5}{6}\)
বা, \(\cfrac{3x+3-2x-2}{6}+\cfrac{2-3}{x+1}=-\cfrac{5}{6}\)
বা, \(\cfrac{x+1}{6}-\cfrac{1}{x+1}=-\cfrac{5}{6}\)
বা, \(\cfrac{(x+1)^2-6}{6(x+1)}=-\cfrac{5}{6}\)
বা, \(\cfrac{x^2+2x+1-6}{(x+1)}=-5\)
বা, \(x^2+2x-5=-5(x+1)\)
বা, \(x^2+2x-5+5x+5=0\)
বা, \(x^2+7x=0\)
বা, \(x(x+7)=0\)

\(\therefore\) হয়, \(x=0\)
নয়, \((x+7)=0\) বা, \(x=-7\)
\(\therefore\) নির্ণেয় সমাধান \(x=0\) অথবা, \(x=-7\) (Answer)