1) \( \frac{\sec \sqrt{13-x}}{x^{4}-4 x^{3}-5 x^{2}-4 x+1}= \)

To simplify the given expression, we first need to analyze the denominator: \(x^4 - 4x^3 - 5x^2 - 4x + 1\). We will look for potential factorization or roots using the Rational Root Theorem or synthetic division. By testing \(x = 1\): \[ 1^4 - 4(1)^3 - 5(1)^2 - 4(1) + 1 = 1 - 4 - 5 - 4 + 1 = -11 \quad \text{(not a root)} \] Now testing \(x = -1\): \[ (-1)^4 - 4(-1)^3 - 5(-1)^2 - 4(-1) + 1 = 1 + 4 - 5 + 4 + 1 = 5 \quad \text{(not a root)} \] Next, we will use polynomial long division to break down the polynomial. By performing synthetic division for possible rational roots or examining coefficients, we aim to factor the polynomial into manageable parts. The denominator can be rewritten or checked for simplification through frameworks such as completing the square or numerical evaluation. However, the given expression \( \frac{\sec \sqrt{13-x}}{x^{4}-4 x^{3}-5 x^{2}-4 x+1} \) suggests that as we explore values for \(x\) where \( \sqrt{13-x} \) is defined (meaning \(x\) must be less than or equal to 13), the secant function \(\sec\) being undefined for odd multiples of \(\pi/2\) will also impact possible values in the numerator and therefore yield undefined results for specific \(x\) values. As such, without further specific objectives (be it finding limits, roots, or simplifications), we can denote: \[ \frac{\sec \sqrt{13-x}}{f(x)}, \quad f(x) = x^{4}-4 x^{3}-5 x^{2}-4 x+1. \] This is how the equation fosters investigation, arousing curiosity around its roots, factors, or graph representation and zeroes!