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\frac{2007\times 2008}{2007\times 2008+2007}
Divide 2007 by \frac{2007\times 2008+2007}{2008} by multiplying 2007 by the reciprocal of \frac{2007\times 2008+2007}{2008}.
\frac{4030056}{2007\times 2008+2007}
Multiply 2007 and 2008 to get 4030056.
\frac{4030056}{4030056+2007}
Multiply 2007 and 2008 to get 4030056.
\frac{4030056}{4032063}
Add 4030056 and 2007 to get 4032063.
\frac{2008}{2009}
Reduce the fraction \frac{4030056}{4032063} to lowest terms by extracting and canceling out 2007.