Question

please solve this problem
answer is:- x=a+b
and x=a+b/2​

Answer 1

Step-by-step explanation:

$\frac{a}{x - b} + \frac{b}{x - a} = 2 \\ \\ = > \frac{a(x - a) + b(x - b)}{(x - b)(x - a)} = 2 \\ \\ = > \frac{ax - {a}^{2} + bx - {b}^{2} }{ {x}^{2} - ax - bx + ab } = 2 \\ \\ = > x(a + b) - ( {a}^{2} + {b}^{2} ) = 2 {x}^{2} - 2ax - bx + 2ab \\ \\ = > 2 {x}^{2} - 2x(a + b) - x(a + b) + {a}^{2} + {b}^{2} + 2ab = 0 \\ = > 2 {x}^{2} - 2x(a + b) - x(a + b) + {(a + b)}^{2} = 0 \\ = > 2x(x - (a + b)) - (a + b)(x - (a + b) = 0 \\ = > (x - a - b)(2x - a - b) = 0$

Therefore,

either | or

x - a - b = 0 | 2x - a - b =0

=> x = a + b | =>2x = a + b

| => x = (a + b)/2

So,

Value of x is (a + b) or (a + b)/2

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