\(x:\dfrac{1}{2}+x:\dfrac{1}{3}+x:\dfrac{1}{4}+x=2010\\ x:\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+1\right)=2010\\ x:\dfrac{25}{12}=2010\\ x=2010\times\dfrac{25}{12}\\ x=\dfrac{8375}{2}\)
\(x:\dfrac{1}{2}+x:\dfrac{1}{3}+x:\dfrac{1}{4}+x=2010\\ x\times2+x\times3+x\times4+x=2010\\ x\times\left(2+3+4+1\right)=2010\\ x\times10=2010\\ x=210\)