Question

can u pls solve this question : a/(x-b)+b/(x-a)=2

Answer 1

$\frac{a}{x - b} + \frac{b}{x - a} = 2 \\ \frac{a(x - a) + b(x - b)}{(x - a)(x - b)} = 2 \\ x(a + b) - ( {a}^{2} + {b}^{2} ) = 2( {x}^{2} - (a + b)x + ab) \\ 2 {x}^{2} - 2(a + b)x + 2ab - (a + b)x + ( {a}^{2} + {b}^{2} ) = 0 \\ 2 {x}^{2} - 3(a + b)x + (a + b) {}^{2} = 0$
solving the problem by quadratic equation
$2 {x}^{2} - 3(a + b)x + (a + b) {}^{2} = 0 \\ d = \sqrt{9(a + b) {}^{2} - 8(a + b) {}^{2} } = (a + b) \\ so \\ x = \frac{3(a + b)( + - )(a + b)}{4} \\ x = \frac{3a + 3b + a+b }{4} = a + b \\ and \\ x = (3a + 3b - a - b) \div 4 \\ = \frac{(a + b)}{2}$
there are 2 value of X....
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