Variable $x$ cannot be equal to $1$ since division by zero is not defined. Multiply both sides of the equation by $3\left(x-1\right)$, the least common multiple of $x-1,3$.
$$3\left(x+\frac{-1}{2}\right)=x-1$$
Fraction $\frac{-1}{2}$ can be rewritten as $-\frac{1}{2}$ by extracting the negative sign.
$$3\left(x-\frac{1}{2}\right)=x-1$$
Use the distributive property to multiply $3$ by $x-\frac{1}{2}$.
$$3x-\frac{3}{2}=x-1$$
Subtract $x$ from both sides.
$$3x-\frac{3}{2}-x=-1$$
Combine $3x$ and $-x$ to get $2x$.
$$2x-\frac{3}{2}=-1$$
Add $\frac{3}{2}$ to both sides.
$$2x=-1+\frac{3}{2}$$
Add $-1$ and $\frac{3}{2}$ to get $\frac{1}{2}$.
$$2x=\frac{1}{2}$$
Divide both sides by $2$.
$$x=\frac{\frac{1}{2}}{2}$$
Express $\frac{\frac{1}{2}}{2}$ as a single fraction.
