SOLUTION: Hello! I need help solving this equation. Write the partial fraction decomposition of the rational expression. 3x-12/(x-3)^2 Thank you

Algebra ->  Equations -> SOLUTION: Hello! I need help solving this equation. Write the partial fraction decomposition of the rational expression. 3x-12/(x-3)^2 Thank you      Log On


   

Question 977096: Hello!
I need help solving this equation.
Write the partial fraction decomposition of the rational expression.
3x-12/(x-3)^2
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283x-12%29%2F%28%28x-3%29%5E2%29+=+A%2F%28x-3%29+%2B+B%2F%28%28x-3%29%5E2%29








%283x-12%29%2F%28%28x-3%29%5E2%29+=+%28A%28x-3%29+%2B+B%29%2F%28%28x-3%29%5E2%29


%283x-12%29%2F%28%28x-3%29%5E2%29+=+%28Ax-3A+%2B+B%29%2F%28%28x-3%29%5E2%29


3x-12+=+Ax-3A+%2B+B


Notice how 3x matches with Ax. So A+=+3.


The -12 matches with -3A%2BB. So,


-12=-3A%2BB


-12=-3%2A3%2BB


-12=-9%2BB


-12%2B9=B


-3=B


B+=+-3


-------------------------------------------------------


Summary:


A+=+3, B+=+-3


This means %283x-12%29%2F%28%28x-3%29%5E2%29+=+A%2F%28x-3%29+%2B+B%2F%28%28x-3%29%5E2%29 turns into %283x-12%29%2F%28%28x-3%29%5E2%29+=+3%2F%28x-3%29+-+3%2F%28%28x-3%29%5E2%29