Matrix/Rational functions/Characteristic polynomial/Exercise

Compute the characteristic polynomial of the matrix

${\begin{pmatrix}{\frac {X^{2}-4X+7}{X-1}}&{\frac {6X-5}{X^{2}-5}}\\{\frac {4X^{2}+3X-2}{6X^{2}-3X}}&{\frac {X^{2}+8X+9}{X^{2}-3X+5}}\end{pmatrix}}$

over the field of rational functions ${}\mathbb {Q} (X)$.

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