Help to simplify rational expressions?

1.
(3x² + 3xy) / (3x² - 3xy)
= 3(x² + xy)/ 3(x² - xy)
= 3x(x + y) / 3x(x - y)
= (x + y) / (x - y)

Restrictions :
Denominator ≠ 0
3x² - 3xy ≠ 0
3x(x - y) ≠ 0
x ≠ 0 and x ≠ y

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2.
[(6x³ - 6x²) / (x⁴ + 5x³)] ÷ [(2x² + 2x - 40) / (3x² - 15x + 12)]
= [6x²(x - 1) / x³(x + 5)] ÷ [2(x² + x - 20) / 3(x² - 5x + 4)]
= [6x²(x - 1) / x³(x + 5)] ÷ [2(x - 4)(x + 5) / 3(x - 1)(x - 4)]
= [6x²(x - 1) / x³(x + 5)] * [3(x - 1)(x - 4) / 2(x - 4)(x + 5)]
= 9(x - 1)² / x(x + 5)²

Restrictions :
Denominators ≠ 0
x⁴ + 5x³ ≠ 0 and 3x² - 15x + 12 ≠ 0 and 2(x - 4)(x + 5) ≠ 0
x³(x + 5) ≠ 0 and 3(x - 1)(x - 4) ≠ 0 and 2(x - 4)(x + 5) ≠ 0
x ≠ 0 and x ≠ -5 and x ≠ 1 and x ≠ 4 and x ≠ -5

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3.
[20x² / (3x² - 75)] * [(25 - x²) / (2x² + 18)]
= [20x² / 3(x² - 25)] * [-(x² - 25) / 2(x² + 9)]
= -10x² / 3(x² + 9)

Restrictions :
Denominators ≠ 0
3x² - 75 ≠ 0 and 2x² + 18 ≠ 0
For all real values of x: 2x² + 18 ≠ 0
Hence, 3x² - 75 ≠ 0
3(x + 5)(x - 5) ≠ 0
x ≠ -5 and x ≠ 5

(3x^2+3xy)/(3x^2-3xy) =
3x[x+y)/[3x(x-y)] =
(x+y)/(x-y) when x ≠ y or 0

You get one question for your money.

(3x² + 3xy) / (3x² - 3xy)
= (x² + xy) / (x² - xy)
= x(x + y) / [x(x - y)]
= (x + y) / (x - y), where x ≠ 0, x ≠ y

For the exclusions look to the given expression, not this simplified form. Clearly x cannot equal y, because (x - y) is the denominator. But x is a factor of the given denominator, so it cannot equal zero. I eliminated it in my last step by dividing above and below by x. That would be an invalid operation if x were zero.

I am sure your heart was in the right place, and you may have written it correctly on paper, but the expression you gave, x+y /x-y, is not equivalent to this. Please have a regard for order of operations.