求一道数学题：x/(1*2)+x/(2*3).+x/(2008*2009）=2008

x(1/1*2+1/2*3+……+1/2008*2009)=2008
x[(1-1/2)+(1/2-1/3)+……+(1/2008-1/2009)]=2008
x(1-1/2009)=2008
x(2008/2009)=2008
x=2008÷(2008/2009)
x=2009