$$\frac{ x+1 }{ 3 } - \frac{ x+2 }{ 4 } + \frac{ x+3 }{ 5 } =1$$
$x=2$
$$20\left(x+1\right)-15\left(x+2\right)+12\left(x+3\right)=60$$
$$20x+20-15\left(x+2\right)+12\left(x+3\right)=60$$
$$20x+20-15x-30+12\left(x+3\right)=60$$
$$5x+20-30+12\left(x+3\right)=60$$
$$5x-10+12\left(x+3\right)=60$$
$$5x-10+12x+36=60$$
$$17x-10+36=60$$
$$17x+26=60$$
$$17x=60-26$$
$$17x=34$$
$$x=\frac{34}{17}$$
$$x=2$$
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