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What two rational expressions sum to 2x-2/x^2-x-12 

 Dec 6, 2022
 #1
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I guess this should look like:  \(\frac{2x-2}{x^2-x-12}\)

 

If so, it can be written as \(\frac{2x-2}{(x-4)(x+3)}\)

 

Express as partial fractions:  \(\frac{2x-2}{(x-4)(x+3)} = \frac{A}{x-4}+\frac{B}{x+3}\)

 

from which we find    

\(A + B = 2\\\\3A-4B=-2\)

 

i'll leave you to find A and B.

 Dec 6, 2022

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