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Solve for x (in terms of a and b) :x/x-b + b/x-a = 2\(\frac{a}{x-b} + \frac{b}{x-a} = 0\) |
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Answer» \(\cfrac{a}{(x-b)}+\cfrac{b}{x-a}\) = 2 \(\cfrac{a(x-a)+b(x-b)}{{(x-b)}(x-a)}\) = 2 a(x − a) + b(x − b) = 2(x − a)(x − b) ax − a2 + bx − b2 = 2(x2 − bx − ax + ab) (a + b)x − a2 − b2 = 2x2 − 2(a + b)x + 2ab = 0 −2x2 + (a + b)x + 2(a + b)x − a2 − b2 − 2ab = 0 2x2 − (a + b)x − 2(a + b)x + (a + b)2 = 0 2x(x − (a + b)) − (a + b)(x − (a + b)) = 0 (x − (a + b))(2x − (a + b)) = 0 x − (a + b) = 0 or, 2x − (a + b) = 0 x = (a + b),x = \(\cfrac{a+b}2\) ∴x = (a + b) \(\cfrac{(a+b)}2\) |
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