Simplify (((x+2)^2)/(x-2))÷((x^2-4)/(2x-4))

Math
(x+2)2x-2÷x2-42x-4
To divide by a fraction, multiply by its reciprocal.
(x+2)2x-2⋅2x-4×2-4
Factor 2 out of 2x-4.
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Factor 2 out of 2x.
(x+2)2x-2⋅2(x)-4×2-4
Factor 2 out of -4.
(x+2)2x-2⋅2x+2⋅-2×2-4
Factor 2 out of 2x+2⋅-2.
(x+2)2x-2⋅2(x-2)x2-4
(x+2)2x-2⋅2(x-2)x2-4
Simplify the denominator.
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Rewrite 4 as 22.
(x+2)2x-2⋅2(x-2)x2-22
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.
(x+2)2x-2⋅2(x-2)(x+2)(x-2)
(x+2)2x-2⋅2(x-2)(x+2)(x-2)
Simplify terms.
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Cancel the common factor of x+2.
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Factor x+2 out of (x+2)2.
(x+2)(x+2)x-2⋅2(x-2)(x+2)(x-2)
Cancel the common factor.
(x+2)(x+2)x-2⋅2(x-2)(x+2)(x-2)
Rewrite the expression.
x+2x-2⋅2(x-2)x-2
x+2x-2⋅2(x-2)x-2
Cancel the common factor of x-2.
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Factor x-2 out of 2(x-2).
x+2x-2⋅(x-2)⋅2x-2
Cancel the common factor.
x+2x-2⋅(x-2)⋅2x-2
Rewrite the expression.
(x+2)2x-2
(x+2)2x-2
Multiply x+2 and 2x-2.
(x+2)⋅2x-2
Move 2 to the left of x+2.
2(x+2)x-2
2(x+2)x-2
Simplify (((x+2)^2)/(x-2))÷((x^2-4)/(2x-4))

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