Find the partial fraction decomposition. 36/x^3+3x^2

Question

Find the partial fraction decomposition.

 

36/(x^3+3x^2)

 

Not quite sure of the proper way to write that out.

Thank You

Answer 1

x³ + 3x² = x²(x+3).  The term x² requires 2 terms A/x + B/x²

 

So that

36/(x³ + 3X²) = A/x + B/x² + C/(x+3)

 

I let you do the math solving for A, B, and C.

 

Here are the answers for you to check

A = -4

B = 12

C = 4

 

Have fun!

Answer 2

36/(x³+3x^2) ... {REVISED--I misread the denominator and thus made the stupid statement that "DENOMINATOR is not factorable"--Mea Culpa--I thought there was a constant on the end.I HAVE NOW CLEANED MY GLASSES; are you sure it's a cubic?