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The equation given in the question is

(2/x - 2) + (7/x^2 - 4) = (5/x)
(2/x-2) + (7/(x + 2)(x - 2) = (5/x)
2(x + 2) + 7/(x+ 2)(x - 2) = 5/x
(2x + 4 + 7)/(x + 2) (x - 2) = 5/x
(2x + 11)x = 5x^2 - 20
2x^2 + 11x = 5x^2 - 20
5x^2 - 2x^2 - 11x - 20 = 0
3x^2 - 11x - 20 = 0
(3x + 4) (x - 5) = 0
Either 
x = -4/3
or
x = 5
From the above deduction, it can be easily concluded that the correct option among all the options that are given in the question is the first option or option "a".

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