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 start by factoring the expression in the numerator and denominator:

\( \frac{6x^3}{x-5} = \frac{6x^3}{x-5} \)

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

Now, we can rewrite the expression as:

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

Next, we can simplify by canceling out the common factors in the numerator and denominator:

Cancel out \( x-5 \) in the numerator and denominator:

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

Now simplify further by canceling out common factors of 6 and 18:

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

Finally, we simplify by canceling out a factor of x in the numerator and the denominator:

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

Therefore, the simplified expression is \( \frac{x^2 + 5x}{3} \).