Write the form of the partial fraction decomposition of the function do not determine the numerical values of the coefficients. 1/x^4-2401
x^4-2401 = (x^2+49)(x^2-49) = (x^2+49)(x+7)(x-7)
So, you will wind up with
(Ax+B)/(x^2+49) + C/(x+7) + D/(x-7)