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\(\cfrac{1}{x}-\cfrac{1}{3}=\cfrac{1}{x+2}-\cfrac{1}{5}\)
বা, \(\cfrac{1}{x}-\cfrac{1}{x+2}=\cfrac{1}{3}-\cfrac{1}{5}\)
বা, \(\cfrac{x+2-x}{x(x+2)}=\cfrac{5-3}{15}\)
বা, \(\cfrac{2}{x^2+2x}=\cfrac{2}{15}\)
বা, \(\cfrac{1}{x^2+2x}=\cfrac{1}{15}\)
বা, \(x^2+2x=15\)
বা, \(x^2+2x-15=0\)
বা, \(x^2+(5-3)x-15=0\)
বা, \(x^2+5x-3x-15=0\)
বা, \(x(x+5)-3(x+5)=0\)
বা, \((x+5)(x-3)=0\)
হয়, \((x+5)=0\) বা, \(x=-5\)
নয়, \((x-3)=0\) বা, \(x=3\)

\(\therefore\) নির্ণেয় সমাধান, \(x=-5\) এবং \(x=3\) (Answer)