To simplify the expression \( 15x^5 - 3x^3 + \frac{9x^2}{3x} \), we can start by simplifying the term \( \frac{9x^2}{3x} \).
- Simplify \( \frac{9x^2}{3x} \): \[ \frac{9x^2}{3x} = \frac{9}{3} \cdot \frac{x^2}{x} = 3x^{2-1} = 3x \]
Now, we can rewrite the original expression with this simplification: \[ 15x^5 - 3x^3 + 3x \]
- Next, we will combine the terms in standard form. The standard form for polynomials is usually written with the terms ordered from the highest degree to the lowest degree. This means arranging them by their exponent value:
So, arranging the terms, we have: \[ 15x^5 - 3x^3 + 3x \]
Thus, the final simplified expression in standard form is: \[ \boxed{15x^5 - 3x^3 + 3x} \]