Question

What is the partial fraction decomposition of 16/(x³-4x²)

A.a/x+b/x-4
B.a/x+b/x+4
C.a/x-4+b/x+4
D.a/x-2+b/x+2

Answer 1

To decompose the expression 16/(x³-4x²) into partial fractions, factor the denominator and then equate the numerators on both sides to find the values of A and B.

Step-by-step explanation:

The given expression is 16/(x³-4x²). To decompose this expression into partial fractions, we need to factor the denominator.

Step 1: Factor the denominator as x²(x-4).

Step 2: Write the expression as the sum of two fractions with denominators of x² and x-4 respectively: 16/(x²(x-4)) = A/x² + B/(x-4).

Step 3: To find the values of A and B, multiply both sides of the equation by the common denominator (x²(x-4)).

Step 4: Simplify the equation and compare the numerators on both sides.

Step 5: Solve for A and B by equating the coefficients of x² and x-4 respectively.

So, the partial fraction decomposition of 16/(x³-4x²) is A/x² + B/(x-4).