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
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.
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