Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$-\dfrac{3}{4}$
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 $3$ to $x$ in the equation above to obtain: $f(3)/g(3) \\= (f/g)(3) \\=\dfrac{-2(3)+3}{3^2-5} \\=\dfrac{-6+3}{9-5} \\=\dfrac{-3}{4} \\=-\dfrac{3}{4}$