# Simplify ( square root of 3-2)/( square root of 3+2)+( square root of 3+2)/( square root of 3-2) 3-23+2+3+23-2
Simplify each term.
Multiply 3-23+2 by 3-23-2.
3-23+2⋅3-23-2+3+23-2
Multiply 3-23+2 and 3-23-2.
(3-2)(3-2)(3+2)(3-2)+3+23-2
Expand the denominator using the FOIL method.
(3-2)(3-2)32+3⋅-2+23-4+3+23-2
Simplify.
(3-2)(3-2)-1+3+23-2
Move the negative one from the denominator of (3-2)(3-2)-1.
-1⋅((3-2)(3-2))+3+23-2
Rewrite -1⋅((3-2)(3-2)) as -((3-2)(3-2)).
-((3-2)(3-2))+3+23-2
Expand (3-2)(3-2) using the FOIL Method.
Apply the distributive property.
-(3(3-2)-2(3-2))+3+23-2
Apply the distributive property.
-(33+3⋅-2-2(3-2))+3+23-2
Apply the distributive property.
-(33+3⋅-2-23-2⋅-2)+3+23-2
-(33+3⋅-2-23-2⋅-2)+3+23-2
Simplify and combine like terms.
Simplify each term.
Combine using the product rule for radicals.
-(3⋅3+3⋅-2-23-2⋅-2)+3+23-2
Multiply 3 by 3.
-(9+3⋅-2-23-2⋅-2)+3+23-2
Rewrite 9 as 32.
-(32+3⋅-2-23-2⋅-2)+3+23-2
Pull terms out from under the radical, assuming positive real numbers.
-(3+3⋅-2-23-2⋅-2)+3+23-2
Move -2 to the left of 3.
-(3-2⋅3-23-2⋅-2)+3+23-2
Multiply -2 by -2.
-(3-23-23+4)+3+23-2
-(3-23-23+4)+3+23-2
-(7-23-23)+3+23-2
Subtract 23 from -23.
-(7-43)+3+23-2
-(7-43)+3+23-2
Apply the distributive property.
-1⋅7-(-43)+3+23-2
Multiply -1 by 7.
-7-(-43)+3+23-2
Multiply -4 by -1.
-7+43+3+23-2
Multiply 3+23-2 by 3+23+2.
-7+43+3+23-2⋅3+23+2
Multiply 3+23-2 and 3+23+2.
-7+43+(3+2)(3+2)(3-2)(3+2)
Expand the denominator using the FOIL method.
-7+43+(3+2)(3+2)32+3⋅2-23-4
Simplify.
-7+43+(3+2)(3+2)-1
Move the negative one from the denominator of (3+2)(3+2)-1.
-7+43-1⋅((3+2)(3+2))
Rewrite -1⋅((3+2)(3+2)) as -((3+2)(3+2)).
-7+43-((3+2)(3+2))
Expand (3+2)(3+2) using the FOIL Method.
Apply the distributive property.
-7+43-(3(3+2)+2(3+2))
Apply the distributive property.
-7+43-(33+3⋅2+2(3+2))
Apply the distributive property.
-7+43-(33+3⋅2+23+2⋅2)
-7+43-(33+3⋅2+23+2⋅2)
Simplify and combine like terms.
Simplify each term.
Combine using the product rule for radicals.
-7+43-(3⋅3+3⋅2+23+2⋅2)
Multiply 3 by 3.
-7+43-(9+3⋅2+23+2⋅2)
Rewrite 9 as 32.
-7+43-(32+3⋅2+23+2⋅2)
Pull terms out from under the radical, assuming positive real numbers.
-7+43-(3+3⋅2+23+2⋅2)
Move 2 to the left of 3.
-7+43-(3+2⋅3+23+2⋅2)
Multiply 2 by 2.
-7+43-(3+23+23+4)
-7+43-(3+23+23+4)
-7+43-(7+23+23)
-7+43-(7+43)
-7+43-(7+43)
Apply the distributive property.
-7+43-1⋅7-(43)
Multiply -1 by 7.
-7+43-7-(43)
Multiply 4 by -1.
-7+43-7-43
-7+43-7-43
Subtract 7 from -7.
-14+43-43
Subtract 43 from 43.
-14+0