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Leaders Manchester City dropped points away at Burnley as they drew 1-1.
Rivals United closed the gap to 13 points with a 2-0 home win against Huddersfield.
Arsenal’s new-look side crushed Everton 5-1 at home with Pierre-Emerick Aubameyang getting off the mark.
At the bottom of the table, Swansea climbed out of the relegation zone with a 1-1 draw at Leicester.
Below are highlights for all of Saturday’s action.
Burnley 1-1 Manchester City: Johann Berg Gudmundsson leaves it late to cancel out Danilo’s stunning first-half strike
Bournemouth 1-2 Burnley: Chris Wood and Robbie Brady strike to rocket Clarets up to sixth in the Premier League
Brighton 3-1 West Ham: Jose Izquierdo curls in beauty to lift Seagulls three points clear of drop
Leicester 1-1 Swansea: Federico Fernandez rescues point for Carlos Carvajal’s men after Jamie Vardy opens scoring
Manchester United 2-0 Huddersfield: Alexis Sanchez scores his first goal for Red Devils as Huddersfield’s relegation fears increase
West Brom 2-3 Southampton: Mauricio Pellegrino’s side seal comeback win to ease sack fears
Arsenal 5-1 Everton: Aaron Ramsey scores first ever hat-trick as Pierre-Emerick Aubameyang nets
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