Roger Federer, Serena Williams fly into last eight
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Murray called it a "tough situation" but he admitted his mind was already on his next match, a quarter-final with France's world number 36 Jeremy Chardy. The Briton is scheduled to face Federer in the semi-finals.
"I felt after the first few games, because he wasn't serving hard at all, you know, his forehand side wasn't moving that well either," said Murray of Simon.
"It was just about trying to finish the match as quickly as I could and then getting ready for the next one."
Chardy, who comes from the same coaching stable as Williams, reached his first Grand Slam quarter-final with a straight-sets defeat of Italian Andreas Seppi. He had never previously gone past the second round in Melbourne.
Jo-Wilfried Tsonga, buoyed by new coach Roger Rasheed, beat Richard Gasquet in four sets to tee up a quarter-final against Federer.
Meanwhile the women's competition hotted up as Williams ran over a stunned Maria Kirilenko 6-2, 6-0 and her potential semi-final opponent, title-holder Victoria Azarenka, dominated Elena Vesnina 6-1, 6-1.
Williams dispatched Kirilenko in less than an hour as she reached her 35th Grand Slam quarter-final and set up a last-eight clash with fellow American Sloane Stephens, 19, who beat Serbia's Bojana Jovanovski.
"I haven't beaten Serena and I hope I'll give you all a good show," said the confident teenager.
Russian veteran Svetlana Kuznetsova, a two-time Grand Slam winner, missed much of last season with injury but she said the break had done her good as she returned and beat ex-number one Caroline Wozniacki in three sets.
She said: "After 10 years of travelling I was getting tired. But I'm feeling fresh again and very happy to be in the quarter-finals because I struggled last year."
In Wednesday's quarter-finals, Kuznetsova will meet last year's champion Azarenka.
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