Answer
$$\frac{\left(x+1\right)\left(3x+2\right)}{2\left(x+5\right)\left(2x-3\right)}$$
Work Step by Step
Recall, multiplying rational expressions means that you multiply the numerators by each other and also multiply the denominators by each other to get the new numerator and denominator, respectively. Thus, we find:
$$ \frac{\left(15x^2-65x-50\right)\left(x^2+2x+1\right)}{\left(2x^2-x-3\right)\left(10x^2-250\right)}\\ \frac{\left(x+1\right)\left(x-5\right)\left(3x+2\right)}{2\left(x+5\right)\left(x-5\right)\left(2x-3\right)}\\\ \frac{\left(x+1\right)\left(3x+2\right)}{2\left(x+5\right)\left(2x-3\right)}$$
