The integers G and H are chosen such that
G/(x + 5) + H/(x^2 - 4x) = (3x^2 - 13x - 5)/(x^3 + x^2 - 20x)
for all values of x except -5, 0, and 4. Find H/G.
See many, many integer solutions here:
https://www.wolframalpha.com/input/?i=y%2F%28x%2B5%29%2Bz%2F%28x%5E2-4*x%29%3D%283*x%5E2-13*x-5%29%2F%28x%5E3%2Bx%5E2-20*x%29%2C+integer+solution
+118608 G/(x + 5) + H/(x^2 - 4x) = (3x^2 - 13x - 5)/(x^3 + x^2 - 20x)
\(\frac{G}{(x + 5) }+ \frac{H}{(x^2 - 4x)} = \frac{(3x^2 - 13x - 5)}{(x^3 + x^2 - 20x)}\\ \frac{G}{(x + 5) }+ \frac{H}{x(x - 4)} = \frac{(3x^2 - 13x - 5)}{x(x+5)(x-4)}\\ \frac{G*x(x - 4)+H(x+5)}{{x(x+5)(x-4)} }= \frac{(3x^2 - 13x - 5)}{x(x+5)(x-4)}\\ G*x(x - 4)+H(x+5)=3x^2 - 13x - 5\)
Expand then simplify the LHS
Then equate coefficients
