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

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SUMMARY

The discussion focuses on solving the transformation problem for variables a and b in the equation 1/(z+a) = (a/z) + [b/(1-z)]. A participant suggests substituting two different values for z to create a system of equations, which can then be solved for a and b. The context indicates that the participants are not yet familiar with Laplace transforms, which are typically used for such transformations. This approach simplifies the problem into manageable algebraic equations.

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LakeMountD
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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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