{(x - a)/(x - b)} + {(x - b)/(x - a)} = (a/b) + (b/a) হলে , x = ?

প্রশ্ন: (x - a)/(x - b) + (x - b)/(x - a) = a/b + b/a হলে , x = ?<br /><br />সমাধান: <br />(x - a)/(x - b) + (x - b)/(x - a) = a/b + b/a <br />⇒ (x - a)/(x - b) - a/b = b/a - (x - b)/(x - a)<br />⇒ (bx- ab - ax + ab)/b(x - b) = (bx- ab - ax + ab)/a(x - a)<br />⇒ b(x - b) = a(x - a)<br />⇒ bx - b² = ax - a²<br />⇒ bx - ax = b² - a²<br />⇒ x(b-a) = (b+a)(b-a)<br />∴ x = a + b