# Multiply (15/( square root of 6-1)+4/( square root of 6-2)-12/(3- square root of 6))*( square root of 6+11)

(156-1+46-2-123-6)⋅(6+11)
Simplify terms.
Simplify each term.
Multiply 156-1 by 6+16+1.
(156-1⋅6+16+1+46-2-123-6)⋅(6+11)
Multiply 156-1 and 6+16+1.
(15(6+1)(6-1)(6+1)+46-2-123-6)⋅(6+11)
Expand the denominator using the FOIL method.
(15(6+1)62+6-6-1+46-2-123-6)⋅(6+11)
Simplify.
(15(6+1)5+46-2-123-6)⋅(6+11)
Cancel the common factor of 15 and 5.
Factor 5 out of 15(6+1).
(5(3(6+1))5+46-2-123-6)⋅(6+11)
Cancel the common factors.
Factor 5 out of 5.
(5(3(6+1))5(1)+46-2-123-6)⋅(6+11)
Cancel the common factor.
(5(3(6+1))5⋅1+46-2-123-6)⋅(6+11)
Rewrite the expression.
(3(6+1)1+46-2-123-6)⋅(6+11)
Divide 3(6+1) by 1.
(3(6+1)+46-2-123-6)⋅(6+11)
(3(6+1)+46-2-123-6)⋅(6+11)
(3(6+1)+46-2-123-6)⋅(6+11)
Apply the distributive property.
(36+3⋅1+46-2-123-6)⋅(6+11)
Multiply 3 by 1.
(36+3+46-2-123-6)⋅(6+11)
Multiply 46-2 by 6+26+2.
(36+3+46-2⋅6+26+2-123-6)⋅(6+11)
Multiply 46-2 and 6+26+2.
(36+3+4(6+2)(6-2)(6+2)-123-6)⋅(6+11)
Expand the denominator using the FOIL method.
(36+3+4(6+2)62+6⋅2-26-4-123-6)⋅(6+11)
Simplify.
(36+3+4(6+2)2-123-6)⋅(6+11)
Cancel the common factor of 4 and 2.
Factor 2 out of 4(6+2).
(36+3+2(2(6+2))2-123-6)⋅(6+11)
Cancel the common factors.
Factor 2 out of 2.
(36+3+2(2(6+2))2(1)-123-6)⋅(6+11)
Cancel the common factor.
(36+3+2(2(6+2))2⋅1-123-6)⋅(6+11)
Rewrite the expression.
(36+3+2(6+2)1-123-6)⋅(6+11)
Divide 2(6+2) by 1.
(36+3+2(6+2)-123-6)⋅(6+11)
(36+3+2(6+2)-123-6)⋅(6+11)
(36+3+2(6+2)-123-6)⋅(6+11)
Apply the distributive property.
(36+3+26+2⋅2-123-6)⋅(6+11)
Multiply 2 by 2.
(36+3+26+4-123-6)⋅(6+11)
Multiply 123-6 by 3+63+6.
(36+3+26+4-(123-6⋅3+63+6))⋅(6+11)
Multiply 123-6 and 3+63+6.
(36+3+26+4-12(3+6)(3-6)(3+6))⋅(6+11)
Expand the denominator using the FOIL method.
(36+3+26+4-12(3+6)9+36-36-62)⋅(6+11)
Simplify.
(36+3+26+4-12(3+6)3)⋅(6+11)
Cancel the common factor of 12 and 3.
Factor 3 out of 12(3+6).
(36+3+26+4-3(4(3+6))3)⋅(6+11)
Cancel the common factors.
Factor 3 out of 3.
(36+3+26+4-3(4(3+6))3(1))⋅(6+11)
Cancel the common factor.
(36+3+26+4-3(4(3+6))3⋅1)⋅(6+11)
Rewrite the expression.
(36+3+26+4-4(3+6)1)⋅(6+11)
Divide 4(3+6) by 1.
(36+3+26+4-(4(3+6)))⋅(6+11)
(36+3+26+4-(4(3+6)))⋅(6+11)
(36+3+26+4-(4(3+6)))⋅(6+11)
Apply the distributive property.
(36+3+26+4-(4⋅3+46))⋅(6+11)
Multiply 4 by 3.
(36+3+26+4-(12+46))⋅(6+11)
Apply the distributive property.
(36+3+26+4-1⋅12-(46))⋅(6+11)
Multiply -1 by 12.
(36+3+26+4-12-(46))⋅(6+11)
Multiply 4 by -1.
(36+3+26+4-12-46)⋅(6+11)
(36+3+26+4-12-46)⋅(6+11)
(3+56+4-12-46)⋅(6+11)
(7+56-12-46)⋅(6+11)
Subtract 12 from 7.
(-5+56-46)⋅(6+11)
(-5+56-46)⋅(6+11)
Subtract 46 from 56.
(-5+6)⋅(6+11)
(-5+6)⋅(6+11)
(-5+6)⋅(6+11)
Expand (-5+6)(6+11) using the FOIL Method.
Apply the distributive property.
-5(6+11)+6(6+11)
Apply the distributive property.
-56-5⋅11+6(6+11)
Apply the distributive property.
-56-5⋅11+66+6⋅11
-56-5⋅11+66+6⋅11
Simplify and combine like terms.
Simplify each term.
Multiply -5 by 11.
-56-55+66+6⋅11
Combine using the product rule for radicals.
-56-55+6⋅6+6⋅11
Multiply 6 by 6.
-56-55+36+6⋅11
Rewrite 36 as 62.
-56-55+62+6⋅11
Pull terms out from under the radical, assuming positive real numbers.
-56-55+6+6⋅11
Move 11 to the left of 6.
-56-55+6+116
-56-55+6+116
-55+6+66
-49+66
-49+66
The result can be shown in multiple forms.
Exact Form:
-49+66
Decimal Form:
-34.30306154…
Multiply (15/( square root of 6-1)+4/( square root of 6-2)-12/(3- square root of 6))*( square root of 6+11)

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