Help with some math? I don't understand this

I have already spent at least 20 minutes on these, but I don't understand how to get the answer. I looked in my book. I am not asking for the answers I just want to know how to do them so I can get the answer. Thanks
1.What is the excluded value of the rational expression 2x+6/ 4x-8
2.What is the simplified form of x^4-81/x+3

Excluded value refers to a value that would cause a denominator to become 0 (zero). Write a little equation: 4x – 8 = 0 and see that x = 2. Whatever else happens, 2 cannot be an answer.
Difference of squares: First, x cannot be –3, since that would cause a zero in the denominator. Then factor the numerator: (x² + 9)(x² + 9) = (x² + 9)(x + 3)(x – 3)/(x + 3). That leaves (x² + 9)(x – 3).

1) RULE: You cannot divide a function by 0. Never.

So the excluded value is going to be the value at which the denominator equals 0.

2) I would say to simplify this function, divide the numerator by the denominator using long division and then this will help you factorise it.

excluded value of the rational expression (2x + 6)/(4x - 8)
the value of denominator is not zero i.e. (4x – 8) is not zero
i.e. 4x is not equal to 8
i.e. x is not equal to 2

x^4 – 81/(x + 3)
= (x² + 9)(x² – 9)/(x + 3)
= (x² + 9)(x + 3)(x – 3)/(x + 3)
= (x² + 9)(x – 3)
= x³ – 3x² + 9x – 27
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1. x cannot equal 2, or your denominator would be zero.

2. Factor the numerator by the difference of squares

(x² - 9)(x² + 9)/(x + 3)

Then again

(x + 3)(x - 3)(x² + 9) / (x + 3)

Let the (x + 3)'s cancel.

(x - 3)(x² + 9)

1)

(2*(x + 3)/(4*(x - 2))

When x = 2, x - 2 = 0; therefore, x ≠ 2

2)

(x^4 - 81)/(x + 3) = (x^2 + 9)*(x + 3)*(x - 3)/(x + 3) = (x^2 + 9)*(x - 3), answer!