1. The problem statement, all variables and given/known data Hello! Here is my second post on the subject partial fraction decomposition. The subject looks pretty easy to learn, but when I try exercises, I do not get to the correct answer. Please, take a look at the exercise below and help me to see my mistakes. 2. Relevant equations (-2x^2 + 20x - 68) / (x^3 + 4x^2 + 4x + 16) 3. The attempt at a solution Step 1: create a form for partial fraction decomposition by factoring the denominator: x^3 + 4x^2 + 4x + 16 = (x^2 + 4) ( x + 4) x^2 + 4 is in irreducible quadratic form, thus I will work with the above factors Step 2: clear denominators (-2x^2 + 20x - 68) (x^2 + 4) ( x + 4) / (x^3 + 4x^2 + 4x + 16) = A (x^2 + 4) ( x + 4) / (x + 4) + (Bx + C) (x^2 + 4) ( x + 4) / (x^2 + 4) -2x^2 + 20x - 68 = x^2 (A + B) + x ( C + 4B) + 4C + 4A Step 3: find values of A, B, C A + C = -2 C + 4B = 20 4C + 4A = -68 (A + C) = -17 Matrix A 1 0 1 0 1 4 1 0 1 Matrix B -2 20 -17 And the determinant of matrix A is zero, hence I can't solve the task using Cramer's rule. Obviously, there are mistakes in my approach. What are they? Please, help me to see them. Thank you!