SOLUTION: Write the partial fraction decomposition of the following rational expression. {{{ (8x^2+10x+20)/x(x+4)(x+5) }}}

Write the partial fraction decomposition of the following rational expression.


The other person is WRONG!!

 = 
 =  --- Multiplying right-side by LCD, x(x + 4)(x + 5)

 --- Equating NUMERATORS, since DENOMINATORS are same
 ------ Substituting - 5 for x, to determine the value of C
8(25) - 50 + 20 = 0 + 0 + C(- 5)(- 5 + 4)
  200 - 50 + 20 = C(- 5)(- 1)
            170 = 5C
            = 34 = C


 ------ Substituting - 4 for x, to determine the value of B
8(16) - 40 + 20 = 0 + B(- 4)(- 4 + 5) + 0
  128 - 40 + 20 = B(- 4)(1)
            108 = - 4B
           = - 27 = B


 ------ Substituting 1 for x, 34 for C, and - 27 for B, to determine the value of A
8(1) + 10 + 20 = A(5)(6) - 27(1)(6) + 34(1)(5)
   8 + 10 + 20 = 30A - 162 + 170
            38 = 30A + 8
        38 - 8 = 30A
            30 = 30A
            = 1 = A

So, (A, B, C)  = (1, - 27, 34)

We then get:  =  =