Answer
$\frac{p^2+8p}{(2p+1)(p-5)(3p-2)}$
Work Step by Step
Step 1. Factor each denominator, we have $2p^2-9p-5=(2p+1)(p-5)$ and $6p^2-p-2=(2p+1)(3p-2)$
Step 2. The least common denominator can be identified as $(2p+1)(p-5)(3p-2)$
Step 3. Convert each expression to have the least common denominator then perform operations:
$\frac{p(3p-2)}{(2p+1)(p-5)(3p-2)}-\frac{2p(p-5)}{(2p+1)(p-5)(3p-2)}=\frac{p^2+8p}{(2p+1)(p-5)(3p-2)}$
