How to Solve a Transformation Problem for Variables a and b?

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Find a & b for the following transformation

1/(z+a) = (a/z) + [b/(1-z)]

I am kind of lost as to where to start on this and google didn't help much typing in math transformations. I know how to do laplace transforms and such but not really sure what they are asking here and we aren't to Laplace yet.
 
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Why don't you just set z to two different values then solve the resulting pair of equations for a and b?
 

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