Answer
$\frac{5x-18}{4x(x+6)}$
Work Step by Step
First, we find the least common multiple of the denominators of the fractions. This, upon inspection, is found to be $4x(x+6)$. Then, we use the least common multiple to create a common denominator, allowing us to subtract the fractions:
$\frac{2x}{x^{2}+6x}-\frac{3}{4x}$
=$\frac{2x}{x(x+6)}-\frac{3}{4x}$
=$\frac{4(2x)-3(x+6)}{4x(x+6)}$
=$\frac{8x-3x-18}{4x(x+6)}$
=$\frac{5x-18}{4x(x+6)}$
