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 can first factor the quadratic terms in the denominators:

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

Next, simplify further by canceling out the common factors:

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

This can be further simplified by dividing both the numerator and denominator by 6:

\(\frac{6x^2(x+5)}{18x} = \frac{x^2(x+5)}{3x} = \frac{x(x+5)}{3}\)

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