Bill F. answered • 01/13/13

Experienced Teacher & Tutor in Round Rock, TX

I read your question as [(3x+9) / (2x-6)] * [(4x+4) / (x+3)]. Assuming that's correct:

Multiply both numerators and both denominators:

(12x^{2} + 12x +36x + 36) / (2x^{2} + 6x - 6x - 18)

= (12x^{2} + 48x + 36) / (2x^{2} -18).

Factor: 12(x^{2} + 4x + 3) / 2(x^{2} - 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