solve 1/a+b+x = 1/a + 1/b+ 1/x, a+b is not = 0
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1/(a + b + x) = 1/a + 1/b + 1/x
=> 1/(a + b + x) - 1/x = 1/a + 1/b
Take LCM on both the sides
=> (x - a - b - x)/x(a + b + x) = (a + b)/ab
=> -(a + b)/ax + bx + x^2 = (a + b)/ab
(a + b) is common on both sides of the equation. Cancel them. (-) sign is taken common from the LHS.
=> -ab = ax + bx + x^2
=> x^2 + ax + bx + ab = 0
=> x(x + a) + b(x + a) = 0
=> (x + b)(x + a) = 0
=> x = -b, -a
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