# Divide ((x^4-16)/(x^3+27))/((x+2)/(2x+6))

x4-16×3+27x+22x+6
Multiply the numerator by the reciprocal of the denominator.
x4-16×3+27⋅2x+6x+2
Simplify the numerator.
Rewrite x4 as (x2)2.
(x2)2-16×3+27⋅2x+6x+2
Rewrite 16 as 42.
(x2)2-42×3+27⋅2x+6x+2
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)x3+27⋅2x+6x+2
Simplify.
Rewrite 4 as 22.
(x2+4)(x2-22)x3+27⋅2x+6x+2
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)x3+27⋅2x+6x+2
(x2+4)(x+2)(x-2)x3+27⋅2x+6x+2
(x2+4)(x+2)(x-2)x3+27⋅2x+6x+2
Simplify the denominator.
Rewrite 27 as 33.
(x2+4)(x+2)(x-2)x3+33⋅2x+6x+2
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2) where a=x and b=3.
(x2+4)(x+2)(x-2)(x+3)(x2-x⋅3+32)⋅2x+6x+2
Simplify.
Multiply 3 by -1.
(x2+4)(x+2)(x-2)(x+3)(x2-3x+32)⋅2x+6x+2
Raise 3 to the power of 2.
(x2+4)(x+2)(x-2)(x+3)(x2-3x+9)⋅2x+6x+2
(x2+4)(x+2)(x-2)(x+3)(x2-3x+9)⋅2x+6x+2
(x2+4)(x+2)(x-2)(x+3)(x2-3x+9)⋅2x+6x+2
Cancel the common factor of x+2.
Factor x+2 out of (x2+4)(x+2)(x-2).
(x+2)((x2+4)(x-2))(x+3)(x2-3x+9)⋅2x+6x+2
Cancel the common factor.
(x+2)((x2+4)(x-2))(x+3)(x2-3x+9)⋅2x+6x+2
Rewrite the expression.
(x2+4)(x-2)(x+3)(x2-3x+9)(2x+6)
(x2+4)(x-2)(x+3)(x2-3x+9)(2x+6)
Multiply (x2+4)(x-2)(x+3)(x2-3x+9) and 2x+6.
(x2+4)(x-2)(2x+6)(x+3)(x2-3x+9)
Factor 2 out of 2x+6.
Factor 2 out of 2x.
(x2+4)(x-2)(2(x)+6)(x+3)(x2-3x+9)
Factor 2 out of 6.
(x2+4)(x-2)(2x+2⋅3)(x+3)(x2-3x+9)
Factor 2 out of 2x+2⋅3.
(x2+4)(x-2)(2(x+3))(x+3)(x2-3x+9)
(x2+4)(x-2)⋅2(x+3)(x+3)(x2-3x+9)
Cancel the common factor of x+3.
Cancel the common factor.
(x2+4)(x-2)⋅2(x+3)(x+3)(x2-3x+9)
Rewrite the expression.
(x2+4)(x-2)⋅2×2-3x+9
(x2+4)(x-2)⋅2×2-3x+9
Move 2 to the left of (x2+4)(x-2).
2(x2+4)(x-2)x2-3x+9
Divide ((x^4-16)/(x^3+27))/((x+2)/(2x+6))