We prove special cases of the Ratios Conjecture for the family of quadratic Dirichlet
L
L
-functions over function fields. More specifically, we study the average of
L
(
1
/
2
+
α
,
χ
D
)
/
L
(
1
/
2
+
β
,
χ
D
)
L(1/2+\alpha ,\chi _D)/L(1/2+\beta ,\chi _D)
, when
D
D
varies over monic, square-free polynomials of degree
2
g
+
1
2g+1
over
F
q
[
x
]
\mathbb {F}_q[x]
, as
g
→
∞
g \to \infty
, and we obtain an asymptotic formula when
ℜ
β
≫
g
−
1
/
2
+
ε
\Re \beta \gg g^{-1/2+\varepsilon }
. We also study averages of products of
2
2
over
2
2
and
3
3
over
3
3
L
L
-functions, and obtain asymptotic formulas when the shifts in the denominator have real part bigger than
g
−
1
/
4
+
ε
g^{-1/4+\varepsilon }
and
g
−
1
/
6
+
ε
g^{-1/6+\varepsilon }
respectively. The main ingredient in the proof is obtaining upper bounds for negative moments of
L
L
-functions. The upper bounds we obtain are expected to be almost sharp in the ranges described above.