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Greece Junior Math Olympiad
1989 Greece Junior Math Olympiad
4
alg. simplifications - Greece Juniors 1989 p4
alg. simplifications - Greece Juniors 1989 p4
Source:
September 14, 2024
algebra
simplification
Problem Statement
Simplifyi)
1
+
2
a
+
2
a
a
+
1
a
1+\frac{2a+\dfrac{2}{a}}{a+\dfrac{1}{a}}
1
+
a
+
a
1
2
a
+
a
2
ii)
3
b
+
3
b
+
3
b
2
b
+
1
b
+
1
b
2
\frac{3b+\dfrac{3}{b}+\dfrac{3}{b^2}}{b+\dfrac{1}{b}+\dfrac{1}{b^2}}
b
+
b
1
+
b
2
1
3
b
+
b
3
+
b
2
3
iii)
(
1
a
2
+
1
b
2
+
1
a
b
)
a
6
b
2
−
a
6
−
a
5
b
a
4
b
\frac{\left(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{ab}\right)a^6b^2-a^6-a^5b}{a^4b}
a
4
b
(
a
2
1
+
b
2
1
+
ab
1
)
a
6
b
2
−
a
6
−
a
5
b
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