If we know that x is an integer and 2x + 3 + 23 − x + 2x + 18x2 − 9 is an integer, then x is () A. 2 b. 3 C. 4 d. 5

The original formula = 2 (x − 3) − 2 (x + 3) + 2x + 18 (x + 3) (x − 3) = 2 (x + 3) (x + 3) (x − 3) = 2x − 3, when x-3 = 2, i.e. x = 5, the original formula value is an integer; when x-3 = 1, i.e. x = 4, the original formula value is an integer; when x-3 = - 1, i.e. x = 2, the original formula value is an integer; when x-3 = - 2, i.e. x = 1, the original formula value is an integer, the symbol

Given that x is an integer and 2 / x + 3 + 2 / 3-x + 2x = 18 / x ^ 2-9 is an integer, find all x values that meet the conditions

2/(x+3)+2/(3-x)+(2x+18)/(x^2-9)
=[2(x-3)-2(x+3)+(2x+18)]/(x^2-9)
=(2x+6)/(x^2-9)
=2 / (x-3) is an integer
So, x-3 = 2,1, - 1, - 2
x=5,4,2,1

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