first, factorise each expression.
3 + -2 = 13+−2=1
3 * -2 = -63⋅−2=−6
x^2 + x - 6 = (x+3)(x-2)x2+x−6=(x+3)(x−2)
3 + 3 = 63+3=6
3 * 3 = 93⋅3=9
x^2 + 6x + 9 = (x+3)(x+3)x2+6x+9=(x+3)(x+3)
for the other two expressions, the identity (a+b)(a-b) = a^2-b^2(a+b)(a−b)=a2−b2 can be used.
x^2 - 4 = x^2 - 2^2x2−4=x2−22
= (x+2)(x-2)=(x+2)(x−2)
x^2 - 9 = x^2 - 3^2x2−9=x2−32
= (x+3)(x-3)=(x+3)(x−3)
putting the factorised expressions into the question gives
((x+3)(x-2))/((x+2)(x-2)) * ((x+3)(x-3))/((x+3)(x+3))(x+3)(x−2)(x+2)(x−2)⋅(x+3)(x−3)(x+3)(x+3)
this can be cancelled
((x+3)cancel((x-2)))/((x+2)cancel((x-2))) * (cancel((x+3))(x-3))/(cancel((x+3))(x+3))
((x+3))/((x+2)) * ((x-3))/((x+3))
(cancel((x+3)))/((x+2)) * ((x-3))/(cancel((x+3)))
to give 1/(x+2) * (x-3)/1
this is the same as (x-3)/(x+2)