The Anfield club are currently seven points behind Manchester United in the title race.
Barrichello and new world champion Jenson Button dominated the early part of this year's title race with Brawn.
It was also suggested they were unhappy with losing ground to Manchester United in the Premiership title race.
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Meanwhile, Arsenal goalkeeper Manuel Almunia believes this season could see the tightest Premier League title race in years.
Ford's Mikko Hirvonen took second ahead of Spain's Dani Sordo, who consolidated his third place in the title race.
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But the appeal was ruled inadmissible, leaving him just one point clear in the Formula One world title race.
Hamilton leads the title race by three points from Webber, with Vettel, Button and Alonso needing to make up ground.
Jousting for the championship is obviously a step too far for James, but what a title race we have in prospect.
However, he hinted that his players were struggling to deal with the big points deficit they face in the title race.
Reigning champions Barcelona lead the Spanish title race with rivals Real Madrid five points behind them with nine matches to go.
Hamilton has a seven-point lead in the title race which means Massa must win or finish second to deny him the title.
In the title race, Button has 15 points, five more than Barrichello.
Deep into stoppage time, his goal had tied the game at 1-1, costing United two points in the English Premier League title race.
April 30th 2012 Manchester United fans where mourning the loss to our neighbours Manchester City, a loss that changed everything in the title race.
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Mancini's side may have dropped out of the title race but are in a strong position in both the Europa League and FA Cup.
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Following assistant manager Ray Wilkins's dismissal in November, Chelsea took only six points from seven league games and fell behind in the title race.
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Carlo Ancelotti's men visit Old Trafford on Saturday for a clash that could have a decisive influence on the outcome of the title race.
Scot Alister McRae is on the verge of a home victory in the production class which would put him top of the title race.
The FIA president said that Hamilton and Alonso would have been thrown out of the Formula One title race if he had got his way.
Victory for Ancelotti's Blues on Tuesday will move them four points clear of United in the Premier League title race, with four games to go.
Celtic coach Neil Lennon said this week that his side's recent championship successes make them better equipped to triumph in this season's SPL title race.
Rossi now leads Melandri by 58 points in the title race.
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The Spaniard finished runner-up to Valentino Rossi in last year's title race and his build-up to the new season has been disrupted by a fractured hand.
In the English Premier League title race, leaders Manchester United were stunned 1-0 at struggling Wigan Wednesday to give chasing Manchester City a glimmer of hope.
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Finland's Kimi Raikkonen, the closest challenger to Vettel in this year's title race, was fourth fastest in his Lotus ahead of Brazilian Felipe Massa in the second Ferrari.
The Brazilian also said Brawn's championship leader Jenson Button must cope with the "pressure" of leading the title race better if he is to land the 2009 crown.
The Light Blues headed into the customary tough test in the Granite City hoping leaders Celtic would slip up at Tannadice, with the title race reaching epic proportions.
He will possibly team up in Bamako with Sevilla's Fredi Kanoute, whose team are also still in the Spanish title race despite being two points behind the leading pair.
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In Sunday's other match with a bearing on the title race, Arsenal continued their fine start to the season with a 6-2 home win over Blackburn at the Emirates.
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