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

Algebra ->  Trigonometry-basics -> SOLUTION: Write the partial fraction decomposition of the following rational expression. {{{ (8x^2+10x+20)/x(x+4)(x+5) }}}      Log On


   

Question 1162547: Write the partial fraction decomposition of the following rational expression.
+%288x%5E2%2B10x%2B20%29%2Fx%28x%2B4%29%28x%2B5%29+
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!




Multiply by the least common denominator....

A%28x%2B4%29%28x%2B5%29%2BB%28x%29%28x%2B5%29%2BC%28x%29%28x%2B4%29+=+8x%5E2%2B10x%2B20
A%28x%5E2%2B9x%2B20%29%2BB%28x%5E2%2B5x%29%2BC%28x%5E2%2B4x%29+=+8x%5E2%2B10x%2B20

Equate coefficients:

(1) A%2BB%2BC+=+8
(2) 9A%2B5B%2B4C+=+10
(3) 20A+=+20

Equation (3) immediately gives us A=1. Substituting in (1) and (2) gives us

(4) B%2BC+=+7
(5) 5B%2B4C+=+1

Solve by elimination....

4B%2B4C+=+28
4B%2B5C+=+1
C+=+-27

Then

B+=+34

ANSWER: