Simplify ( square root of 3+1)/(1- square root of 3)*( square root of 3+1)/( square root of 3+1)

Math
3+11-3⋅3+13+1
Cancel the common factor of 3+1.
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Cancel the common factor.
3+11-3⋅3+13+1
Rewrite the expression.
11-3⋅(3+1)
11-3⋅(3+1)
Multiply 11-3 by 1+31+3.
11-3⋅1+31+3⋅(3+1)
Simplify terms.
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Multiply 11-3 and 1+31+3.
1+3(1-3)(1+3)⋅(3+1)
Expand the denominator using the FOIL method.
1+31+3-3-32⋅(3+1)
Simplify.
1+3-2⋅(3+1)
Move the negative in front of the fraction.
-1+32⋅(3+1)
Apply the distributive property.
-1+323-1+32⋅1
Combine 3 and 1+32.
-3(1+3)2-1+32⋅1
Simplify the expression.
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Multiply -1 by 1.
-3(1+3)2-1+32
Combine the numerators over the common denominator.
-3(1+3)-(1+3)2
-3(1+3)-(1+3)2
-3(1+3)-(1+3)2
Simplify the numerator.
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Apply the distributive property.
-3⋅1-33-(1+3)2
Multiply -1 by 1.
-3-33-(1+3)2
Multiply -33.
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Raise 3 to the power of 1.
-3-(313)-(1+3)2
Raise 3 to the power of 1.
-3-(3131)-(1+3)2
Use the power rule aman=am+n to combine exponents.
-3-31+1-(1+3)2
Add 1 and 1.
-3-32-(1+3)2
-3-32-(1+3)2
Simplify each term.
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Rewrite 32 as 3.
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Use axn=axn to rewrite 3 as 312.
-3-(312)2-(1+3)2
Apply the power rule and multiply exponents, (am)n=amn.
-3-312⋅2-(1+3)2
Combine 12 and 2.
-3-322-(1+3)2
Cancel the common factor of 2.
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Cancel the common factor.
-3-322-(1+3)2
Divide 1 by 1.
-3-31-(1+3)2
-3-31-(1+3)2
Evaluate the exponent.
-3-1⋅3-(1+3)2
-3-1⋅3-(1+3)2
Multiply -1 by 3.
-3-3-(1+3)2
-3-3-(1+3)2
Apply the distributive property.
-3-3-1⋅1-32
Multiply -1 by 1.
-3-3-1-32
Subtract 3 from -3.
-3-1-232
Subtract 1 from -3.
-4-232
-4-232
Cancel the common factor of -4-23 and 2.
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Factor 2 out of -4.
2⋅-2-232
Factor 2 out of -23.
2⋅-2+2(-3)2
Factor 2 out of 2(-2)+2(-3).
2(-2-3)2
Cancel the common factors.
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Factor 2 out of 2.
2(-2-3)2(1)
Cancel the common factor.
2(-2-3)2⋅1
Rewrite the expression.
-2-31
Divide -2-3 by 1.
-2-3
-2-3
-2-3
The result can be shown in multiple forms.
Exact Form:
-2-3
Decimal Form:
-3.73205080…
Simplify ( square root of 3+1)/(1- square root of 3)*( square root of 3+1)/( square root of 3+1)

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