To solve this fraction we have to reduce to the same denominator, but prior to reducing, note that one of the denominators x²-4 could be expanded to:
(x-2)(x+2) [remember a² - b² =n(a-b)(a+c)]
Let the denominator be (x-2)(x+2),
2/(x-2)(x+2) -(x-2)/(x-2)(x+2) = 3(x+2)/ (x-2)(x+2) ==>
2 -(x-2) = 3x+6 ==>2-x+2 = 3x+6 ==> x=-4/6 ==> x= - (1/2)