First, get a common denominator. When you factor x^2-4, you get (x+2) and (x-2), so you can multiply everything by these variables.
3(x+2)/((x-2)(x+2)) + 8/(x^2-4) = (x^2-4)/(x^2-4)
Since the denominators for all of these are the same, we can ignore them. Looking at only the numerators, we have
3(x+2) + 8 = (x^2-4)
Simplified, it's 3x+6+8=x^2-4
Simplify again to get 3x+14=x^2-4
Move everything to one side to have x^2-3x-18=0.
What two numbers multiply together to get -18 and add to get -3? If you said -6 and 3, you're right.
Factor to have (x-6)(x+3). So, x=6 or x=-3. Whew, that was a lot of work. I hope this helps.
3(x+2)/((x-2)(x+2)) + 8/(x^2-4) = (x^2-4)/(x^2-4)
Since the denominators for all of these are the same, we can ignore them. Looking at only the numerators, we have
3(x+2) + 8 = (x^2-4)
Simplified, it's 3x+6+8=x^2-4
Simplify again to get 3x+14=x^2-4
Move everything to one side to have x^2-3x-18=0.
What two numbers multiply together to get -18 and add to get -3? If you said -6 and 3, you're right.
Factor to have (x-6)(x+3). So, x=6 or x=-3. Whew, that was a lot of work. I hope this helps.
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3(x+2)+8 = x^2-4
x^2 -3x - 18 = 0
(x-6)(x+3) = 0
x = 6 and x = -3
x^2 -3x - 18 = 0
(x-6)(x+3) = 0
x = 6 and x = -3
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(3x+14)/(x-2)(x+2)