Question

(\frac{2x^{2}-6x}{3x - 1}div x - 3=)

Explanation:

Step1: Rewrite division as multiplication

$\frac{2x^2 - 6x}{3x - 1} \div (x - 3) = \frac{2x^2 - 6x}{3x - 1} \times \frac{1}{x - 3}$

Step2: Factor numerator of first fraction

Factor $2x$ from $2x^2 - 6x$: $\frac{2x(x - 3)}{3x - 1} \times \frac{1}{x - 3}$

Step3: Cancel common factors

Cancel $(x - 3)$ (where $x
eq 3, x
eq \frac{1}{3}$): $\frac{2x}{3x - 1}$

Answer:

$\frac{2x}{3x - 1}$ (with restrictions $x
eq 3$ and $x
eq \frac{1}{3}$)