If $a$ and $b$ are the roots of the equation ${\mathrm{x}}^2-7\mathrm{x}-1=0$, then the value of $\frac{{\mathrm{a}}^{21}+{\mathrm{b}}^{21}+{\mathrm{a}}^{17}+{\mathrm{b}}^{17}}{{\mathrm{a}}^{19}+{\mathrm{b}}^{19}}$ is equal to ____

$\mathrm{a}+\mathrm{b}=7,\hspace{0.17em}\hspace{0.17em}\mathrm{ab}=-1$and ${\mathrm{a}}^2-1=7\mathrm{a}$
${\mathrm{a}}^4+1-2{\mathrm{a}}^2=49{\mathrm{a}}^2$   $\Rightarrow {\mathrm{a}}^4+1=51{\mathrm{a}}^2$
$\frac{{\mathrm{a}}^{21}+{\mathrm{b}}^{21}+{\mathrm{a}}^{17}+{\mathrm{b}}^{17}}{{\mathrm{a}}^{19}+{\mathrm{b}}^{19}}$  $\mathrm{E}=\frac{{\mathrm{a}}^{17}({\mathrm{a}}^4+1)+{\mathrm{b}}^{17}({\mathrm{b}}^4+1)}{{\mathrm{a}}^{19}+{\mathrm{b}}^{19}}$
$=\frac{{\mathrm{a}}^{17}\left(51{\mathrm{a}}^2\right)+{\mathrm{b}}^{17}\left(51{\mathrm{b}}^2\right)}{{\mathrm{a}}^{19}+{\mathrm{b}}^{19}}$$\Rightarrow \mathrm{E}=51$