Final answer:
To find the partial fraction decomposition of the expression (1)/(x(2x+5)(4x² +1)), assume a form with unknown coefficients for each term, clear the denominators, and solve for the coefficients by equating the powers of x. The additional information provided does not directly apply to the decomposition process.
Step-by-step explanation:
The process of finding the partial fraction decomposition of a rational expression involves rewriting the expression as the sum of simpler fractions. The given expression is (1)/(x(2x+5)(4x² +1)). To decompose it, we assume a form that assigns coefficients:
A/x + (Bx + C)/(2x+5) + (Dx + E)/(4x²+1) = 1/(x(2x+5)(4x²+1))
Next, clear the denominators by multiplying both sides by x(2x+5)(4x²+1), distribute, and collect like terms. Then, equate the coefficients of the powers of x on both sides to find the values of A, B, C, D, and E. This grants us the partial fractions.
However, the provided information and equations do not relate directly to the question at hand and, thus, will not be used for this decomposition. The correct partial fraction decomposition can only be obtained through the described procedure or applicable algebraic techniques.