There is disagreement of the scholars regarding this. The position of the Hanafi school is that it is permitted and recommended to fast the first nine days of Dhu’l Hijja if one can.
However, it would be better not to fast all the days if one somehow thought that this was necessary or binding to do; or if it would impose physical hardship or difficulty, because a small amount of supererogatory (nafl) works performed with sincerity, longing for Allah, love, and thankfulness are better than mountains of works that are stale; or if it would lead to non-fulfillment of the rights of others, such as contractual commitments or family duties.
And Allah alone gives success.
