#### Answer

$\frac{2}{5}$

#### Work Step by Step

Step 1: $\frac{x^{2}+x}{3x}\times\frac{6}{5x+5}$
Step 2: $\frac{x(x+1)}{3x}\times\frac{6}{5(x+1)}$
Step 3: Cancelling $(x+1)$ as it is found in both numerator and denominator, we get $\frac{x}{3x}\times\frac{6}{5}$.
Step 4: Cancelling $(x)$ as it is found in both numerator and denominator, we get $\frac{1}{3}\times\frac{6}{5}$.
Step 5: Now the expression becomes $\frac{6}{3\times5}$.
Step 6: After simplifying, the expression becomes $\frac{2}{5}$.