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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
1985 Iran MO (2nd round)
7
(a+c)/(b+c) > a/b - [Iran Second Round 1985]
(a+c)/(b+c) > a/b - [Iran Second Round 1985]
Source:
December 29, 2010
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
a,b
a
,
b
and
c
c
c
be real numbers with
b
,
c
>
0.
b,c >0.
b
,
c
>
0.
Prove that if
a
<
b
(
a
>
b
)
,
a<b \ ( a>b),
a
<
b
(
a
>
b
)
,
then
a
+
c
b
+
c
>
a
b
(
a
+
c
b
+
c
<
a
b
)
\frac{a+c}{b+c} > \frac ab \qquad ( \frac{a+c}{b+c} < \frac ab)
b
+
c
a
+
c
>
b
a
(
b
+
c
a
+
c
<
b
a
)
And then prove that
a
+
c
b
+
c
\frac{a+c}{b+c}
b
+
c
a
+
c
is between
1
1
1
and
a
b
.
\frac ab.
b
a
.
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