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 need to factor the numerator and denominator, and then cancel out common factors.

First, factor the expressions: \( 6x^3 = 2 \cdot 3 \cdot x \cdot x \cdot x = 2 \cdot 3 \cdot x^3 \) \( x^2 - 25 = (x + 5)(x - 5) \)

Now rewrite the expression: \( \frac{6x^3}{x - 5} \cdot \frac{x^2 - 25}{18x^2} = \frac{2 \cdot 3 \cdot x^3}{x - 5} \cdot \frac{(x + 5)(x - 5)}{2 \cdot 3 \cdot 3 \cdot x \cdot x} \)

Next, cancel out common factors: \( \frac{2 \cdot 3 \cdot x^3}{x - 5} \cdot \frac{(x + 5)(x - 5)}{2 \cdot 3 \cdot 3 \cdot x \cdot x} = \frac{2 \cdot 3 \cdot x^2(x + 5)}{3 \cdot x} \)

Finally, simplify the expression: \( \frac{2 \cdot 3 \cdot x^2(x + 5)}{3 \cdot x} = 2x(x + 5) \)

Therefore, the simplified expression is \( 2x(x + 5) \).