To simplify the expression \(\frac{7x^3 + 4x^2 + 2x}{x^2}\), you can divide each term in the numerator by \(x^2\):
\[ \frac{7x^3}{x^2} + \frac{4x^2}{x^2} + \frac{2x}{x^2} \]
Now simplify each term:
- \(\frac{7x^3}{x^2} = 7x^{3-2} = 7x\)
- \(\frac{4x^2}{x^2} = 4\)
- \(\frac{2x}{x^2} = 2x^{-1} = \frac{2}{x}\)
Putting it all together, we get:
\[ 7x + 4 + \frac{2}{x} \]
Thus, the simplified form of the expression is:
\[ 7x + 4 + \frac{2}{x} \]