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Recalling Basics of Fractions
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Represent the following mixed infinite d
Question
Represent the following mixed infinite decimal periodic fractions as common fractions:
1
+
x
+
x
x
+
1
:
x
2
−
x
1
Hard
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Solution
Verified by Toppr
1
+
x
+
x
x
+
1
:
x
2
−
x
1
=
(
1
+
x
+
x
)
(
x
−
1
)
(
x
+
1
)
(
x
−
1
)
:
x
(
x
2
−
2
1
−
1
)
1
=
(
x
)
3
−
1
(
x
)
2
−
1
×
x
(
x
2
3
−
1
)
=
x
2
3
−
1
(
x
−
1
)
x
(
x
2
3
−
1
)
=
x
(
x
−
1
)
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