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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.

 Feb 7, 2022
 #1
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I believe this requires the use of Partial Fraction Decomposition:

 

As the denominators of the two fractions on the RHS are factors of the denominator on the LHS, you can multiply both sides by x^2-7x+10. You are left with A(x-5) + B(x-2) = 5x+16. You can plug in 5 for x to cancel out A and solve for B. Similarly, you can plug in 2 for x to cancel out B and solve for A. 

 

Let me know if I did anything wrong!

 Feb 7, 2022

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