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There are real numbers $A$ and $B$ such that \[\frac{5x+16}{x^2-7x+10}=\frac{A}{x-2}+\frac{B}{x-5}.\]Find $A+B$.

 Nov 7, 2021
 #1
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Hint: Cross multiply

 Nov 7, 2021
 #2
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Get a common denominator on the RHS

Are the two denominators the same now?  Yes ?

 

So now equate coefficients on the top

 Nov 7, 2021
edited by Melody  Nov 7, 2021

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