3-23+2

Multiply 3-23+2 by 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)

Expand the denominator using the FOIL method.

(3-2)(3-2)32+3⋅-2+23-4

Simplify.

(3-2)(3-2)-1

Move the negative one from the denominator of (3-2)(3-2)-1.

-1⋅((3-2)(3-2))

Rewrite -1⋅((3-2)(3-2)) as -((3-2)(3-2)).

-((3-2)(3-2))

Apply the distributive property.

-(3(3-2)-2(3-2))

Apply the distributive property.

-(33+3⋅-2-2(3-2))

Apply the distributive property.

-(33+3⋅-2-23-2⋅-2)

-(33+3⋅-2-23-2⋅-2)

Simplify each term.

Combine using the product rule for radicals.

-(3⋅3+3⋅-2-23-2⋅-2)

Multiply 3 by 3.

-(9+3⋅-2-23-2⋅-2)

Rewrite 9 as 32.

-(32+3⋅-2-23-2⋅-2)

Pull terms out from under the radical, assuming positive real numbers.

-(3+3⋅-2-23-2⋅-2)

Move -2 to the left of 3.

-(3-2⋅3-23-2⋅-2)

Multiply -2 by -2.

-(3-23-23+4)

-(3-23-23+4)

Add 3 and 4.

-(7-23-23)

Subtract 23 from -23.

-(7-43)

-(7-43)

Apply the distributive property.

-1⋅7-(-43)

Multiply -1 by 7.

-7-(-43)

Multiply -4 by -1.

-7+43

The result can be shown in multiple forms.

Exact Form:

-7+43

Decimal Form:

-0.07179676…

Divide ( square root of 3-2)/( square root of 3+2)