Simplify ((x-5)/(x^2))/((2x-10)/(3x^4))

$\frac{\frac{x - 5}{x^{2}}}{\frac{2 x - 10}{3 x^{4}}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{x - 5}{x^{2}} \cdot \frac{3 x^{4}}{2 x - 10}$

Cancel the common factor of $x^{2}$ .

Factor $x^{2}$ out of $3 x^{4}$ .

$\frac{x - 5}{x^{2}} \cdot \frac{x^{2} (3 x^{2})}{2 x - 10}$

Cancel the common factor.

$\frac{x - 5}{x^{2}} \cdot \frac{x^{2} (3 x^{2})}{2 x - 10}$

Rewrite the expression.

$(x - 5) \frac{3 x^{2}}{2 x - 10}$

Factor $2$ out of $2 x - 10$ .

Factor $2$ out of $2 x$ .

$(x - 5) \frac{3 x^{2}}{2 (x) - 10}$

Factor $2$ out of $- 10$ .

$(x - 5) \frac{3 x^{2}}{2 x + 2 \cdot - 5}$

Factor $2$ out of $2 x + 2 \cdot - 5$ .

$(x - 5) \frac{3 x^{2}}{2 (x - 5)}$

Cancel the common factor of $x - 5$ .

Factor $x - 5$ out of $2 (x - 5)$ .

$(x - 5) \frac{3 x^{2}}{(x - 5) \cdot 2}$

Cancel the common factor.

$(x - 5) \frac{3 x^{2}}{(x - 5) \cdot 2}$

Rewrite the expression.

$\frac{3 x^{2}}{2}$