# Divide (x^4-16)/(x^2+4) x4-16×2+4
Simplify the numerator.
Rewrite x4 as (x2)2.
(x2)2-16×2+4
Rewrite 16 as 42.
(x2)2-42×2+4
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x2 and b=4.
(x2+4)(x2-4)x2+4
Simplify.
Rewrite 4 as 22.
(x2+4)(x2-22)x2+4
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=2.
(x2+4)(x+2)(x-2)x2+4
(x2+4)(x+2)(x-2)x2+4
(x2+4)(x+2)(x-2)x2+4
Cancel the common factor of x2+4.
Cancel the common factor.
(x2+4)(x+2)(x-2)x2+4
Divide (x+2)(x-2) by 1.
(x+2)(x-2)
(x+2)(x-2)
Expand (x+2)(x-2) using the FOIL Method.
Apply the distributive property.
x(x-2)+2(x-2)
Apply the distributive property.
x⋅x+x⋅-2+2(x-2)
Apply the distributive property.
x⋅x+x⋅-2+2x+2⋅-2
x⋅x+x⋅-2+2x+2⋅-2
Combine the opposite terms in x⋅x+x⋅-2+2x+2⋅-2.
Reorder the factors in the terms x⋅-2 and 2x.
x⋅x-2x+2x+2⋅-2
x⋅x+0+2⋅-2
x⋅x+2⋅-2
x⋅x+2⋅-2
Simplify each term.
Multiply x by x.
x2+2⋅-2
Multiply 2 by -2.
x2-4
x2-4
Divide (x^4-16)/(x^2+4)     