SOLUTION: Write the partial fraction decomposition of the rational expression. {{{ x/(x+1)(x+2) }}}

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Question 1162543: Write the partial fraction decomposition of the rational expression.
+x%2F%28x%2B1%29%28x%2B2%29+
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

+x%2F%28x%2B1%29%28x%2B2%29+

+x%2F%28x%2B1%29%28x%2B2%29+=+A%2F%28x%2B1%29%2BB%2F%28x%2B2%29

Multiply through by (x+1)(x+2)

x+=+A%28x%2B2%29%2BB%28x%2B1%29

Substitute x=-2

-2+=+A%28-2%2B2%29%2BB%28-2%2B1%29

-2+=+A%280%29%2BB%28-1%29

-2+=+-B

B=2

Substitute x=-1

-1+=+A%28-1%2B2%29%2B2%28-1%2B1%29

-1+=+A%281%29%2B2%280%29

-1+=+A

+x%2F%28x%2B1%29%28x%2B2%29+=+%28-1%29%2F%28x%2B1%29%2B2%2F%28x%2B2%29

Edwin