8^x-64-3•(4^x^+^1-2^x^+^4)/x^4-x^2-12<0

To simplify the given inequality, we can first rewrite it in a more manageable form:

8^x - 64 - 3*(4^(x+1) - 2^(x+4))/(x^4 - x^2 - 12) < 0

Now, let's simplify the expression inside the brackets:

-3*(4^(x+1) - 2^(x+4)) = -3*(44^x - 2(2^x)^2) = -3*(44^x - 24^x) = -324^x = -6*4^x

Substitute this back into the original inequality:

8^x - 64 - 6*4^x / (x^4 - x^2 - 12) < 0

Now, let's simplify the terms with the same base:

8^x = (2^3)^x = 2^(3x)

64^x = 62^4^x = 6*2^(2x)

So, the inequality becomes:

2^(3x) - 64 - 6 * 2^(2x) / (x^4 - x^2 - 12) < 0

Now, we can factor out common terms:

2^(3x) - 6*2^(2x) - 64 / (x^4 - x^2 - 12) < 0

At this point, you could try different approaches to solve this inequality, such as factorizing or using properties of exponents.