Step-by-step explanation:
First factor all expressions:
Numerator:
(x^2-3x-54)*(x^2+12x+36)
=(x-9)(x+6)*(x+6)(x+6)
=(x-9)(x+6)^3
Denominator:
(x^2-18+81)*(x+6)
=(x-9)(x-9)*(x+6)
We see clearly that the highlighted terms are common factors between the numerator and denominator, and can be cancelled from each PROVIDED that x does not equal 9, nor x does not equal -6.
Thus the resulting simplified expression is
(x+6)^2/(x-9) provided x does not equal 9 nor -6.
