Answer
vertical asymptote $x=-\frac{5}{2}$,
horizontal asymptote $y=\frac{1}{2}$,
oblique asymptote $none$.
Work Step by Step
Step 1. Factor the function $F(x)=\frac{x^2+6x+5}{2x^2+7x+5}=\frac{(x+1)(x+5)}{(x+1)(2x+5)}=\frac{x+5}{2x+5}, (x\ne-1)$,
Step 2. we can find the vertical asymptote $x=-\frac{5}{2}$,
Step 3. we can find the horizontal asymptote $y=\frac{1}{2}$,
Step 4. we can find the oblique asymptote $none$.
