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Problem
Problem
A recent poll showed that nearly 30% of schoolchildren think that
1
2
+
1
3
=
1
+
1
2
+
3
=
2
5
\frac{1}{2}+\frac{1}{3}=\frac{1+1}{2+3}=\frac{2}{5}
2
1
+
3
1
=
2
+
3
1
+
1
=
5
2
. This is wrong, of course. Is it possible that
1
a
+
1
b
=
2
a
+
b
\frac{1}{a}+\frac{1}{b}=\frac{2}{a+b}
a
1
+
b
1
=
a
+
b
2
for some real numbers
a
a
a
and
b
b
b
?
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