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\(\cfrac{1}{(x-2)(x-4)}+\cfrac{1}{(x-4)(x-6)}\)
\(+\cfrac{1}{(x-6)(x-8)}+\cfrac{1}{3}=0\)


বা, \(\cfrac{2}{(x-2)(x-4)}+\cfrac{2}{(x-4)(x-6)}\)

\(+\cfrac{2}{(x-6)(x-8)}+\cfrac{2}{3}=0\) [উভয় পক্ষকে \(2\) দ্বারা গুন করে পাই]

বা, \(\cfrac{(x-2)-(x-4)}{(x-2)(x-4)}+\cfrac{(x-4)-(x-6)}{(x-4)(x-6)}\)
\(+\cfrac{(x-6)-(x-8)}{(x-6)(x-8)}+\cfrac{2}{3}=0\)


বা, \(\cfrac{1}{(x-4)}-\cfrac{1}{(x-2)}+\cfrac{1}{(x-6)}\)
\(-\cfrac{1}{(x-4)}+\cfrac{1}{(x-8)}-\cfrac{1}{(x-6)}+\cfrac{2}{3}=0\)
বা, \(\cfrac{1}{(x-8)}-\cfrac{1}{(x-2)}=-\cfrac{2}{3}\)
বা, \(\cfrac{x-2-x+8}{(x-8)(x-2)}=-\cfrac{2}{3}\)
বা, \(\cfrac{6}{x^2-2x-8x+16}=-\cfrac{2}{3}\)
বা, \(\cfrac{6}{x^2-10x+16}=-\cfrac{2}{3}\)
বা, \(2x^2-20x+32=-18\)
বা, \(2x^2-20x+32+18=0\)
বা, \(2x^2-20x+50=0\)
বা, \(x^2-10x+25=0\)
বা, \(x^2-2.x.5+5^2=0\)
বা, \((x-5)^2=0\)
বা, \((x-5)(x-5)=0\)

\(\therefore \) নির্ণেয় সমাধান \(x=5, 5\)