Basic Math Examples

Simplify ( square root of 3+1)/(1- square root of 3)*( square root of 3+1)/( square root of 3+1)
3+11-33+13+1
Step 1
Cancel the common factor of 3+1.
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Step 1.1
Cancel the common factor.
3+11-33+13+1
Step 1.2
Rewrite the expression.
3+11-31
3+11-31
Step 2
Multiply 3+11-3 by 1.
3+11-3
Step 3
Multiply 3+11-3 by 1+31+3.
3+11-31+31+3
Step 4
Combine fractions.
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Step 4.1
Multiply 3+11-3 by 1+31+3.
(3+1)(1+3)(1-3)(1+3)
Step 4.2
Expand the denominator using the FOIL method.
(3+1)(1+3)1+3-3-32
Step 4.3
Simplify.
(3+1)(1+3)-2
(3+1)(1+3)-2
Step 5
Simplify the numerator.
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Step 5.1
Reorder terms.
(1+3)(1+3)-2
Step 5.2
Raise 1+3 to the power of 1.
(1+3)1(1+3)-2
Step 5.3
Raise 1+3 to the power of 1.
(1+3)1(1+3)1-2
Step 5.4
Use the power rule aman=am+n to combine exponents.
(1+3)1+1-2
Step 5.5
Add 1 and 1.
(1+3)2-2
(1+3)2-2
Step 6
Rewrite (1+3)2 as (1+3)(1+3).
(1+3)(1+3)-2
Step 7
Expand (1+3)(1+3) using the FOIL Method.
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Step 7.1
Apply the distributive property.
1(1+3)+3(1+3)-2
Step 7.2
Apply the distributive property.
11+13+3(1+3)-2
Step 7.3
Apply the distributive property.
11+13+31+33-2
11+13+31+33-2
Step 8
Simplify and combine like terms.
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Step 8.1
Simplify each term.
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Step 8.1.1
Multiply 1 by 1.
1+13+31+33-2
Step 8.1.2
Multiply 3 by 1.
1+3+31+33-2
Step 8.1.3
Multiply 3 by 1.
1+3+3+33-2
Step 8.1.4
Combine using the product rule for radicals.
1+3+3+33-2
Step 8.1.5
Multiply 3 by 3.
1+3+3+9-2
Step 8.1.6
Rewrite 9 as 32.
1+3+3+32-2
Step 8.1.7
Pull terms out from under the radical, assuming positive real numbers.
1+3+3+3-2
1+3+3+3-2
Step 8.2
Add 1 and 3.
4+3+3-2
Step 8.3
Add 3 and 3.
4+23-2
4+23-2
Step 9
Cancel the common factor of 4+23 and -2.
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Step 9.1
Factor 2 out of 4.
2(2)+23-2
Step 9.2
Factor 2 out of 23.
2(2)+2(3)-2
Step 9.3
Factor 2 out of 2(2)+2(3).
2(2+3)-2
Step 9.4
Move the negative one from the denominator of 2+3-1.
-1(2+3)
-1(2+3)
Step 10
Rewrite -1(2+3) as -(2+3).
-(2+3)
Step 11
Apply the distributive property.
-12-3
Step 12
Multiply -1 by 2.
-2-3
Step 13
The result can be shown in multiple forms.
Exact Form:
-2-3
Decimal Form:
-3.73205080
 [x2  12  π  xdx ]