I'm supposed to factor..?

Question

"the factors are already given, divide them.." thats what the paper says

1. (x-3 over 2)^3 times (1 over x-3)^2

2. x^2-9 over x+2 times x^2-4 over x-3

Answer 1

The paper is correct.

(x-3) (x-3) (x-3) * (1/(x-3))  (1/(x-3))

two of them cancel out, leaving:

(x - 3)

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x^2 - 9 = (x + 3) (x - 3)

x^2 - 4 = (x + 2) (x - 2)

(x + 3) (x - 3) / (x + 2) * [ (x+2) (x-2) / (x-3) ]

The x+2's and x-3's cancel leaving:

(x + 3) (x - 2)

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