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Algebra/Algebra simplyfy polynomials

Question

Polynomial problem
I have added an attachment.  Could you show me the steps to solve #3.  Thank you.

Division is the same as the multiplication of the inverse.
1. Inverting and multiplying cancels the (x-2)'s,
so all that's left is -7/5.

2. The second fraction is inverted.  The first fraction has and (x-8)(x+8) on top.
The x-8 terms cancel, leaving the answer.

3. The 2nd fraction factors into (x+8)(x-3).
Since it is divided by x-3, the terms cancel, leaving (x+8).
Dividing the numerator of the first fraction by (x+8) gives x²-6x-9.
That is the same as (x-3)², so one (x-3) term cancels.
That leaves an x-3 in the numerator and and 8 in the denominator.
I believe it also leaves a negative sign.
With that, the answer can be seen.

4. Inverting the second fraction and multiplying cancels the (x-3) term in each fraction.
The answer has a negative sign, a 3 in the numerator, and a 2 in the denominator.

Algebra

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Scott A Wilson

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