8^x-64-3•(4^x+1-2^x+4)/x^4-x^2-12

To simplify the given expression, let's break it down step by step: 1. We see that \(8^x\) can be written as \((2^3)^x = 2^{3x}\). 2. Similarly, \(64\) can be written as \(2^6\). 3. We need to expand the expression \(3•(4^x+1-2^x+4)\): \(3•(4^x + 1 - 2^x + 4) = 3•(2^{2x} + 1 - 2^x + 4)\). 4. Next, simplify the denominators by factoring the denominator \(x^4 - x^2 - 12\): \(x^4 - x^2 - 12 = (x^2 - 4)(x^2 + 3) = (x - 2)(x + 2)(x^2 + 3)\). Now, combining all the above steps, we get the simplified expression: \[\frac{2^{3x} - 2^6 - 3•(2^{2x} + 1 - 2^x + 4)}{(x - 2)(x + 2)(x^2 + 3)}\] This is the simplified version of the given expression.