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\(\cfrac{x}{x+1}+\cfrac{x+1}{x}=2\cfrac{1}{12} \)
বা, \(\cfrac{x^2+(x+1)^2}{x(x+1)} =\cfrac{25}{12} \)
বা, \(\cfrac{x^2+(x^2+2x+1)}{x^2+x}=\cfrac{25}{12} \)
বা, \(\cfrac{x^2+x^2+2x+1}{x^2+x}=\cfrac{25}{12} \)
বা, \(\cfrac{2x^2+2x+1}{x^2+x}=\cfrac{25}{12} \)
বা, \(25x^2+25x=24x^2+24x+12 \)
বা, \(25x^2+25x-24x^2-24x-12=0 \)
বা, \(x^2+x-12=0 \)
বা, \(x^2+(4-3)x-12=0 \)
বা, \(x^2+4x-3x-12=0 \)
বা, \(x(x+4)-3(x+4)=0 \)
বা, \((x+4)(x-3)=0 \)
অর্থাৎ,হয় \((x+4)=0 \therefore x=-4 \)
নয়, \((x-3)=0 \therefore x=3 \)
\(\therefore x=-4\) ও \(x=3\) হল \(\cfrac{x}{x+1}+\cfrac{x+1}{x}=2\cfrac{1}{12}\) দ্বিঘাত সমীকরনের সমাধান ।