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There are real numbers A and B such that (5x + 16)/(x^2 - 7x + 10) = A/(x - 2) + B/(x - 5).  Find A + B.

 Jul 21, 2022
 #1
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Note that   x^2 -7x + 10 =   (x - 2) ( x - 5)

 

Multiply through by the factorized form and we  have

 

5x + 16 =   A ( x - 5)  + B ( x - 2)

 

5x +  16 =   (A + B)x  +  ( -5A - 2B)

 

Equating terms we  see that

 

A + B =   5

 

 

cool cool cool

 Jul 21, 2022

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