$$\frac{x-3}{4}+\frac{x-1}{5}-\frac{x-2}{3}=1$$
$x=11$
$$15\left(x-3\right)+12\left(x-1\right)-20\left(x-2\right)=60$$
$$15x-45+12\left(x-1\right)-20\left(x-2\right)=60$$
$$15x-45+12x-12-20\left(x-2\right)=60$$
$$27x-45-12-20\left(x-2\right)=60$$
$$27x-57-20\left(x-2\right)=60$$
$$27x-57-20x+40=60$$
$$7x-57+40=60$$
$$7x-17=60$$
$$7x=60+17$$
$$7x=77$$
$$x=\frac{77}{7}$$
$$x=11$$
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