Simplify the expression (6x+8)/4 ÷ (x2+3)/(5x2) as a single fraction.

Here's how to simplify the expression:

Step 1: To divide by a fraction, multiply by its reciprocal. $\frac{6x+8}{4} \div \frac{x^2+3}{5x^2} = \frac{6x+8}{4} \times \frac{5x^2}{x^2+3}$

Step 2: Multiply the numerators and the denominators. $\frac{(6x+8) \cdot 5x^2}{4 \cdot (x^2+3)}$

Step 3: Factor out common terms from the numerator. Notice that $6x+8$ can be factored as $2(3x+4)$. $\frac{2(3x+4) \cdot 5x^2}{4(x^2+3)}$

Step 4: Simplify the numerical coefficients. The 2 in the numerator and the 4 in the denominator can be simplified. $\frac{10x^2(3x+4)}{4(x^2+3)} = \frac{5x^2(3x+4)}{2(x^2+3)}$ The expression cannot be simplified further.

The simplified expression is: \frac{5x^2(3x+4){2(x^2+3)}}