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Greece Junior Math Olympiad
1988 Greece Junior Math Olympiad
1
simplify fractions - Greece Juniors 1988 p1
simplify fractions - Greece Juniors 1988 p1
Source:
September 13, 2024
algebra
Problem Statement
i) Simplify
(
a
−
4
a
b
a
+
b
+
b
)
:
(
a
a
+
b
−
b
b
−
a
−
2
a
b
a
2
−
b
2
)
\left(a-\frac{4ab}{a+b}+b\right): \left(\frac{a}{a+b}-\frac{b}{b-a}-\frac{2ab}{a^2-b^2}\right)
(
a
−
a
+
b
4
ab
+
b
)
:
(
a
+
b
a
−
b
−
a
b
−
a
2
−
b
2
2
ab
)
ii) Simplify
2
x
2
−
(
3
a
+
b
)
x
+
a
2
+
a
b
2
x
2
−
(
a
+
3
b
)
x
+
a
b
+
b
2
\frac{2x^2-(3a+b)x+a^2+ab}{2x^2-(a+3b)x+ab+b^2}
2
x
2
−
(
a
+
3
b
)
x
+
ab
+
b
2
2
x
2
−
(
3
a
+
b
)
x
+
a
2
+
ab
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