Question:সমাধান কর: `a/(x - a) + b/(x - b) = (a + b)/(x - a - b)` 

Answer সমাধান: দেওয়া আছে,
      `a/(x - a) + b/(x - b) = (a + b)/(x - a - b)`

  বা, `a/(x - a) + b/(x - b) = a/(z - a - b) + b(x - a - b)`

  বা, `a/(z - a) - a/(z - a - b) = b/(x - a - b) + b/(x - b)`  [ পক্ষাকন্তর করে ]

  বা, `(a(x - a - b) - a(x - a))/((x - a)(x - a - b))= (b(x - b) - b(x - a -b))/((x - a - b)(x - b))`

  বা, `(ax - a^2 - ab + a^2)/((x - a)(x - a - b)) = (bx - b^2 - bx + ab + b^2)/((x - b)(x - a - b))`

  বা, `(- ab)/((x - a)(x - a - b)) = (ab)/((x - b) (x - a - b))`

  বা, `(- 1)/((x - a)(x - a - b)) = 1/((x - b)(x - a - b))`   [ উভয় পক্ষকে `ab` দ্বারা ভাগ করে ]

  বা, `(- 1)/(x - a) = 1/(x - b)`  [ (x - a - b) দ্বারা গুণ করে যেখানে (x - a - b) != 0 ]

  বা, `x - a = - x + b`  [ আড়াগুণন করে ]

  বা, `x + x = a + b`   [ পক্ষান্তর করে ]

  বা, `2x = a + b`

   `:.  x = (a + b)/2`

   `:.` নির্ণেয় সমাধান: `x = (a + b)/2` 

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