#### Answer

$\frac{(x-6)}{2(x+3)}$

#### Work Step by Step

We first factor the numerator and denominator of the fraction:
Step 1: $\frac{x^{2}-6x}{2x^{2}+6x}$
Step 2: $\frac{x(x-6)}{2x(x+3)}$
Finally, we cancel out the common factor of x to obtain:
Step 3: $\frac{(x-6)}{2(x+3)}$