Rational functions/Q/Computing example/Exercise

Compute in ${}\mathbb {Q} (X)$ the following expressions.

1. The product

   ${\frac {2X^{3}-5X^{2}+X-1}{X^{2}-2X+6}}\cdot {\frac {X^{2}+3}{5X^{3}-4X^{2}-7}}.$

2. The sum

   ${\frac {4X^{3}-X^{2}+6X-2}{X^{2}-4X-3}}+{\frac {X^{2}-3}{3X^{2}+5}}.$

3. The inverse of

   ${\frac {6X^{3}-9X^{2}+5X-1}{X^{4}-4X^{3}+3X^{2}-8X-3}}.$

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