To simplify the expression \(\frac{4x^2 + 12x + 8}{4x^2}\), you can divide each term in the numerator by the denominator:
\[ \frac{4x^2}{4x^2} + \frac{12x}{4x^2} + \frac{8}{4x^2} \]
This simplifies to:
\[ 1 + \frac{12}{4x} + \frac{8}{4x^2} \]
Now, simplify the fractions:
\[ 1 + \frac{3}{x} + \frac{2}{x^2} \]
So, the final simplified expression is:
\[ 1 + \frac{3}{x} + \frac{2}{x^2} \]