1/((u^2)-4) = A/(u-2) + B/(u+2)

how do u solve for A and B?

i am told that A and B can be easily solved to be A=.25 B=-.25 but i dont see how to get that. Please help

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- November 27th 2008, 06:21 PMimthatgirlsolving for A and B
1/((u^2)-4) = A/(u-2) + B/(u+2)

how do u solve for A and B?

i am told that A and B can be easily solved to be A=.25 B=-.25 but i dont see how to get that. Please help - November 27th 2008, 06:26 PMMathstud28
Ahh, I'm going to assume that this is partial fractions decomposition? If so you can do this. Multiplying through by gives

Now we use this little trick, if we let we get

And letting gives

The other way is to compare coefficents. Expanding the starred step gives

Now we know that for this expression to be true that each of the coefficients must match. So and . Solving those gives the correct values. - November 27th 2008, 06:29 PMimthatgirl
how do u know to let u=2 and -2?

- November 27th 2008, 06:34 PMMathstud28
Because think about it if you have something like

And you want to isolate either or you want the other one to dissapear, and how do you do that? You make its coefficient zero, so you basically need to use the value of that makes either or zero. In this case it would be to Isolate and for - November 27th 2008, 11:44 PMCaptainBlack