\(H=\dfrac{2^{19}\cdot3^9\cdot5+3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot2^{10}\cdot3^9-2^{20}\cdot3^{10}}\)
\(=\dfrac{2^{19}\cdot3^9\cdot5+2^{18}\cdot3^9\cdot5}{2^{19}\cdot3^9-2^{20}\cdot3^{10}}\)
\(=\dfrac{2^{18}\cdot3^9\cdot5\cdot\left(2+1\right)}{2^{19}\cdot3^9\cdot\left(1-6\right)}\)
\(=\dfrac{1}{2}\cdot\dfrac{5\cdot3}{-5}=-\dfrac{1}{2}\cdot3=-\dfrac{3}{2}\)