The value of the product [(x3-27/(x2-9)] x [(x2+7x+12)/(x2+3x+9)]
[(x3 - 27) / (x2 - 9)] * [x2 + 7x + 12) / (x2 + 3x + 9)]
= [(x3 - 33) / (x2 - 32)] * [x2 + 4x + 3x + 12) / (x2 + 3x + 9)]
= [(x - 3)(x2 + x*3 + 32) / (x + 3) (x - 3)] * [{x(x + 4) + 3(x + 4)} / (x2 + 3x + 9)]
= [(x2 + 3x + 9) / (x + 3)] * [(x + 3)(x + 4) / (x2 + 3x + 9)] //x - 3 cancel out each other in the first term
= x + 4 //x2 + 3x + 9 and x +3 cancel out each other
= [(x3 - 33) / (x2 - 32)] * [x2 + 4x + 3x + 12) / (x2 + 3x + 9)]
= [(x - 3)(x2 + x*3 + 32) / (x + 3) (x - 3)] * [{x(x + 4) + 3(x + 4)} / (x2 + 3x + 9)]
= [(x2 + 3x + 9) / (x + 3)] * [(x + 3)(x + 4) / (x2 + 3x + 9)] //x - 3 cancel out each other in the first term
= x + 4 //x2 + 3x + 9 and x +3 cancel out each other