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The integers $G$ and $H$ are chosen such that

\[\frac{G}{x+5}+\frac{H}{x^2-4x}=\frac{x^2-2x+10}{x^3+x^2-20x}\]
for all real values of  except $-5$, $0$, and $4$. Find $H/G$.

 Feb 15, 2021
 #1
avatar+29193 
+2

cross multiply the left side

 

gx^2 -g 4x + hx + 5 h  =  x^2 -2x+10         so    g = 1   h = 2      take it from here ! cheeky

 Feb 15, 2021

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