(4/x + 2) + (1/x - 2)  =  (5x-6) / (x² - 4)

First, simplify the left side:  4/x + 1/x  =  5/x      and + 2 - 2 = 0.

If you factor  x² - 4 , you get:  (x + 2)(x - 2).

The denominaors have three terms:  x,  x + 2,  and  x - 2.  Since denominators are not allowed to be zero, the numers  0, -2,  and  +2  cannot be answers.

5/x  =  (5x-6) / (x² - 4)

Cross multiply:

5(x² - 4)  =  x(5x-6)

Multiply out:

5x² - 20  =  5x² - 6 x

-20  =  -6x

x  =  10/3

I mean

(4/x+2)+(1/x-2) = (5x-6)/(x^2-4)?

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