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Question 698717: Hi, I need help with a simplification that I need to do every time in a certain type of problem
I basically need to go from equations in the form  to equation in the form 
I need a detailed way to go from the first to the second
Another one would be 
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! To go from to 
you need to find the numbers  and  that make
 true for all  values.
You could work from to  ,
showing how good you are at working with polynomials,
and then write the equations that make the coefficients in the numerator the same:
 and 
That would give you a system of linear equations that you could solve for and .
I prefer a less risky approach, safer from my tendency to mess up work with polynomials.
Since true for all values,
I can use two cunningly-chosen values of to generate two linear equations.
For  , the equation is
 or
For  , I get
I do not even write that, confident that I can do that many calculations in my head without messing up, and just write
 -->  --> 
Next I solve  to get  and 
For  and work well too.
If they did not, I would use some numbers that made the calculations easier, and did not make the denominators zero.
For , the equation is
 -->
For , the equation is
 -->  --> 
Then I solve  to get  and 
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