Answer
$1$
Work Step by Step
RECALL:
$(f/g)(x)=\dfrac{f(x)}{g(x)}$
Thus,
$(f/g)(x) = \dfrac{-2x+3}{x^2-5}$
To evaluate the given expression, substitute $-4$ to $x$ in the equation above to obtain:
$f(-4)/g(-4)
\\= (f/g)(-4)
\\=\dfrac{-2(-4)+3}{(-4)^2-5}
\\=\dfrac{8+3}{16-5}
\\=\dfrac{11}{11}
\\=1$