6 х^3/х-5•х^2-25/18х^2

To simplify the expression \( \frac{6x^3}{x-5} \cdot \frac{x^2 - 25}{18x^2} \), we first need to factor the numerator and denominator where possible.

Factor \( 6x^3 \) as \( 2 \cdot 3 \cdot x \cdot x \cdot x \) = \( 2 \cdot 3 \cdot x^3 \).

Factor \( x^2 - 25 \) as a difference of squares: \( (x^2 - 5^2) \) = \( (x+5)(x-5) \).

So, the expression becomes:

\( \frac{2 \cdot 3 \cdot x^3}{x-5} \cdot \frac{(x+5)(x-5)}{18x^2} \).

Next, we can cancel common factors between the numerator and denominator:

\( \frac{6x^3}{x-5} \cdot \frac{x^2 - 25}{18x^2} = \frac{2 \cdot 3 \cdot x^3}{x-5} \cdot \frac{(x+5)(x-5)}{18x^2} = \frac{6x^3}{18x^2} \).

Finally, simplify the expression to get the final answer.

\( \frac{6x^3}{18x^2} = \frac{1}{3}x \).

Therefore, the simplified expression is \( \frac{1}{3}x \).