SOLUTION: please help... Write the partial fraction decomposition of the rational expression: -3x/(x+2)(x+5)

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Question 41071: please help...
Write the partial fraction decomposition of the rational expression:
-3x/(x+2)(x+5)
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Set it up like this
-3x/(x+2)(x+5) = A/(x+2) + B/(x+5)
Now multiply throught by the LCD and get
-3x = A(x+5) + B(x+2)
-3x = Ax + 5A + Bx + 2B
-3x = (A+B)x + (5A + 2B)
Therefore,
5A + 2B = 0 and
A + B = -3
Solve this system by multiplying the bottom eqn by -2 and adding...
5A + 2B = 0
-2A - 2B = 6
we get
3A = 6
A = 2
B = -5
now plug A and B in the first equation above and we're done...