\(\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}=\frac{x+1}{5}+\frac{x+1}{6}\)
=> \(60.\frac{x+1}{2}+60.\frac{x+1}{3}+60.\frac{x+1}{4}=60.\frac{x+1}{5}+60.\frac{x+1}{6}\)
( chiệt tiêu )
=> \(30\left(x+1\right)+20\left(x+1\right)+15\left(x+1\right)=12\left(x+1\right)+10\left(x+1\right)\)
=> \(30x+30+20x+20+15x+15=12x+12+10x+10\)
=> \(65x+65=22x+22\)
=> \(65x-22x=22-65\)
=> \(43x=-43x\)
=> \(x=43:\left(-43\right)=-1\)
Vậy \(x\in\left\{-1\right\}\)
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