Simplify the complex fraction. (1 point) Responses Image with alt text: twelve x plus four over x squared plus three x Image with alt text: four x over three x plus nine Image with alt text: four x over three x squared plus to x plus three none of the above

Answer 1

The simplified complex fraction is:
\[ \frac{12x + 4}{x^2 + 3x} \div \frac{4x}{3x + 9} \]
To divide fractions, multiply the numerator by the reciprocal of the denominator:
\[ \frac{12x + 4}{x^2 + 3x} \times \frac{3x + 9}{4x} \]
Simplify the expression by canceling out common factors:
\[ \frac{4(3x + 1)}{x(x + 3)} \times \frac{3(x + 3)}{4x} \]
\[ \frac{3(3x + 1)}{x(x + 3)} \]
Therefore, the simplified complex fraction is:
\[ \frac{3(3x + 1)}{x(x + 3)} \]