write a simplified expression for the area of the rectangle. State all restrictions on x
I read your question as [(3x+9) / (2x-6)] * [(4x+4) / (x+3)]. Assuming that's correct:
Multiply both numerators and both denominators:
(12x2 + 12x +36x + 36) / (2x2 + 6x - 6x - 18)
= (12x2 + 48x + 36) / (2x2 -18).
Factor: 12(x2 + 4x + 3) / 2(x2 - 9) = 12(x+3)(x+1) / 2(x+3)(x-3)
Divide numerator and denominator by 2(x+3): 6(x+1) / (x-3).
Since a denominator cannot = 0, x cannot = +3, because if x=+3, then (x-3) = (+3-3) = 0