# Simplify (x^3-8)/(2-x)

x3-82-x
Simplify the numerator.
Rewrite 8 as 23.
x3-232-x
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=x and b=2.
(x-2)(x2+x⋅2+22)2-x
Simplify.
Move 2 to the left of x.
(x-2)(x2+2⋅x+22)2-x
Raise 2 to the power of 2.
(x-2)(x2+2x+4)2-x
(x-2)(x2+2x+4)2-x
(x-2)(x2+2x+4)2-x
Simplify terms.
Cancel the common factor of x-2 and 2-x.
Factor -1 out of x.
(-1(-x)-2)(x2+2x+4)2-x
Rewrite -2 as -1(2).
(-1(-x)-1(2))(x2+2x+4)2-x
Factor -1 out of -1(-x)-1(2).
-1(-x+2)(x2+2x+4)2-x
Reorder terms.
-1(-x+2)(x2+2x+4)-x+2
Cancel the common factor.
-1(-x+2)(x2+2x+4)-x+2
Divide -1(x2+2x+4) by 1.
-1(x2+2x+4)
-1(x2+2x+4)
Rewrite -1(x2+2x+4) as -(x2+2x+4).
-(x2+2x+4)
Apply the distributive property.
-x2-(2x)-1⋅4
-x2-(2x)-1⋅4
Simplify.
Multiply 2 by -1.
-x2-2x-1⋅4
Multiply -1 by 4.
-x2-2x-4
-x2-2x-4
Simplify (x^3-8)/(2-x)

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