= Solution
Let $m=\rho_1u_1=\rho_2u_2$ be the signed mass flux. Momentum conservation gives
$$
m^2\left(\frac1{\rho_1}-\frac1{\rho_2}\right)=p_2-p_1.
$$
Dividing the energy-flux equation by $m$ and eliminating $m^2$ yields the <pressure-density Hugoniot relation for a perfect gas>:
$$
\frac{\gamma}{\gamma-1}\left(\frac{p_2}{\rho_2}-\frac{p_1}{\rho_1}\right)
=\frac{p_2-p_1}{2}\left(\frac1{\rho_1}+\frac1{\rho_2}\right).
$$
With $P=p_2/p_1$ and $D=\rho_2/\rho_1$, this becomes
$$
\frac{2\gamma}{\gamma-1}(P-D)=(P-1)(D+1).
$$
Solving for the <mass density> ratio gives
$$
\boxed{D=\frac{(\gamma+1)P+\gamma-1}{(\gamma-1)P+\gamma+1}.}
$$
For a compressive <normal shock wave>, $P>1$ and $D>1$; as $P\to\infty$, the finite <shock compression ratio> is $(\gamma+1)/(\gamma-1)$.
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