Verified answer

( x + 4 ) ( x + 2 ) ( x - 4 ) ( x + 4 )

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( x - 2 ) ( x. + 2 )

( x + 4 )² ( x - 4 )

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x - 2

(x² + 8x + 16) ( x - 4)

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x - 2

x³ - 4x² + 8x² - 32x + 16x - 64

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x - 2

x³ + 4x² - 16x - 64

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x - 2

2 | 1_______4______- 16 _______-64

_ I________2________12_______-8

_ I 1_______6_______- 4________-72

x² + 6x - 4 - 72/(x - 2)

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Are you learning from these questions or are we just doing your homework for you?

Presuming we have a polynomial divided by a fraction:

(x² + 6x + 8) / [(x² - 4) / (x² - 16)]

The first thing I would do is turn the division of the fraction into the multiplication of the reciprocal:

(x² + 6x + 8) * [(x² - 16) / (x² - 4)]

Now factor what you can:

(x + 4)(x + 2) (x + 4)(x - 4) / [(x + 2)(x - 2)]

Then cancel out the common factors in the numerator and denominator (x + 2):

(x + 4)(x + 4)(x - 4) / (x - 2)

Then simplify to get your final result:

(x + 4)(x² - 16) / (x - 2)

(x³ + 4x² - 16x - 64) / (x - 2)