Task 207
Task 207: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. 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 $x$ except $-5$, $0$, and $4$. Find $H/G$.
The task
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 $x$ except $-5$, $0$, and $4$. Find $H/G$.