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*(4*4^x - 2*(2^x)^2) = -3*(4*4^x - 2*4^x) = -3*2*4^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) 6*4^x = 6*2^4^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.