Partial fraction Decomposition 7x 15x2 6x 9 6x2 3x 5x3

Partial fraction Decomposition -7x - 15/x^2 + 6x + 9 -6x^2 + 3x + 5/x^3 - x -4x^4 - 26x^2 - 2x^3 - 8x - 44/(x + 1)(x^2 + 3)^2

Solution

5)(-7x -15)_/(x²+6x+9)

=(-7x -15)_/(x+3)²

let (-7x -15)_/(x+3)²= A_/(x+3) +B_/(x+3)²

(-7x -15)_/(x+3)²= [A(x+3)+B]_/(x+3)²

(-7x -15)_/(x+3)²= [Ax+(3A+B)]_/(x+3)²

A=-7

3A+B =-15

3(-7)+ B=-15

-21+B =-15

B =6

(-7x -15)_/(x+3)²= -7_/(x+3) +6_/(x+3)²

therefore (-7x -15)_/(x²+6x+9) = -7_/(x+3) +6_/(x+3)²