simplify 3 by 4-√3 + 2 by 4+√3
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Answer:
Given expression is
3
+
6
3
2
−
6
+
2
4
3
+
2
+
3
6
On rationalizing each term and using the property (a−b)(a+b)=a
2
−b
2
for each denominator, we get:
(
3
)
2
−(
6
)
2
3
2
(
3
−
6
)
−
(
6
)
2
−(
2
)
2
4
3
(
6
−
2
)
+
(
2
)
2
−(
3
)
2
6
(
2
−
3
)
=
−3
3
6
−3
12
−
4
4
18
−
6
+
−1
12
−
18
=
12
12
12
−12
6
−12
18
+3
6
−12
12
+12
18
=
12
−9
6
=
4
−3
6
Hence,
3
+
6
3
2
−
6
+
2
4
3
+
2
+
3
6
=
4
−3
6
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