Solve for: /((\frac{){x} 3-1)} x-1

Expression: $$\frac { ( \frac { x } { 3 } - 1 ) } { x - 1 }$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{3}{3}$.

$$\frac{\frac{x}{3}-\frac{3}{3}}{x-1}$$

Since $\frac{x}{3}$ and $\frac{3}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-3}{3}}{x-1}$$

Express $\frac{\frac{x-3}{3}}{x-1}$ as a single fraction.

$$\frac{x-3}{3\left(x-1\right)}$$

Use the distributive property to multiply $3$ by $x-1$.

$$\frac{x-3}{3x-3}$$