We need to simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

[(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

use x^2 - 4 = (x - 2)(x +2), also let's find the factors of x^2+3x+2

=> [(x^2 + 2x + x +2)/(x-2)]*[(x - 2)(x + 2)/(x-1)]

=> [(x + 2)(x + 1)/(x - 2)]*[(x - 2)(x + 2)/(x-1)]

cancel the common terms in...

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We need to simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

[(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

use x^2 - 4 = (x - 2)(x +2), also let's find the factors of x^2+3x+2

=> [(x^2 + 2x + x +2)/(x-2)]*[(x - 2)(x + 2)/(x-1)]

=> [(x + 2)(x + 1)/(x - 2)]*[(x - 2)(x + 2)/(x-1)]

cancel the common terms in the numerator and denominator

=> (x + 2)^2*(x + 1)/(x - 1)

**The simplified form of the given expression is (x + 2)^2*(x + 1)/(x - 1)**