Yes, Manchester United will definitely find it difficult to really compete with Manchester City next season. Even though Manchester United has currently recruited new players such as Leni Yoro and Joshua Jirkjee, I also believe that Manchester United will still have difficulty competing with Manchester City. Because as we know, Manchester City is a very solid, compact team and has a great coach like Guardiola. The proof is that Manchester City managed to win the Premier League several seasons in a row. So with these facts it is clear that next season Manchester United will have difficulty competing with Manchester City for the top position in the Premier League. However, if they can enter the top 4, maybe Manchester United still has a little hope next season. The reason is that to compete for the top 4 positions, Manchester United only needs to compete with teams like Liverpool, Aston Villa, Tottenham and Chelsea. Even though it is difficult to compete with these teams, in my opinion Manchester United still has hope of occupying 4th place in the Premier League, if Ten Hag and the current Manchester United players play optimally next season.
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Buying a lot of new players does not mean becoming better, ten Hag did it before, in the previous off-season they also bought a lot of new players, but despite this they had an even worse season. New players need time to adapt, to play with the team, all this takes time, and competitors will get ahead. I think that nothing will change for Manchester United, their main goal at the end of the season will be to get into the top 4, but this may not be easy, because there are teams that are progressing better like Aston Villa, which you mentioned, and Tottenham, Newcastle and Manchester United will fight for the Europa League, that's what I think.
Yes, I agree with your opinion that the adaptation factor is something that cannot be avoided if a team recruits new players and that is what Manchester United is experiencing this season. The reason is that in the transfer market last summer, Manchester United bought several expensive players such as Rasmus Hojlund and Mason Mount. However, as a result, Manchester United is getting worse in the Premier League this season. So as you said, this is definitely caused by the player's poor adaptation factor. Maybe if the Manchester United players who joined last summer can adapt completely, maybe Manchester United can be a little better next season. However, this still cannot guarantee that Manchester United can shine next season. Because in essence it is not the only factor that makes a team shine. However, many factors are needed for a football team to be able to produce excellent performance. So we'll see what Manchester United will be like in the next season, whether it will move in a positive direction or move in a more negative direction. If it moves in a positive direction, Ten Hag will definitely continue to get a contract extension. But if for example Manchester United moves in a more negative direction, I think Ten Hag could be fired by Manchester United in the middle of the season.