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6(202^100+1)^2 + 3(202^100-2)^2 - 3(202^200+8) / 2((202^100+1)^2 - 200^100 - 200^200) (202^100-1)

First, let's simplify the expression inside the parentheses:

(202^100+1)^2 = 202^200 + 2202^100 + 1 (202^100-2)^2 = 202^200 - 4202^100 + 4 (202^100+1)^2 - 200^100 - 200^200 = 202^200 + 2*202^100 + 1 - 200^100 - 200^200

Now, substitute these values back into the original expression:

6(202^200 + 2202^100 + 1) + 3(202^200 - 4202^100 + 4) - 3(202^200 + 8) / 2(202^200 + 2*202^100 + 1 - 200^100 - 200^200)(202^100-1)

Simplify further:

6202^200 + 12202^100 + 6 + 3202^200 - 12202^100 + 12 - 3202^200 - 24 / 2(202^200 + 2202^100 + 1 - 200^100 - 200^200)(202^100-1)

Combine like terms:

6202^200 + 3202^200 - 3202^200 + 12202^100 - 12202^100 - 12 + 6 + 12 - 24 / 2(202^200 + 2202^100 + 1 - 200^100 - 200^200)(202^100-1)

Simplify further:

6202^200 + 12202^100 + 6 + 12 - 24 / 2(202^200 + 2*202^100 + 1 - 200^100 - 200^200)(202^100-1)

Now, you can simplify the expression further by performing the operations indicated.