Final answer:
To fully simplify the expression (x^(2)+14x+40)/(9x-x^(2))*(3)/(x^(2)+6x+8)*(x^(2)-7x-18)/(-x-10), factorize and cancel out common factors between the numerator and denominator.
Step-by-step explanation:
To fully simplify the expression (x^(2)+14x+40)/(9x-x^(2))*(3)/(x^(2)+6x+8)*(x^(2)-7x-18)/(-x-10), we need to factorize and cancel out common factors between the numerator and denominator. The expression can be simplified as follows:
- Factorize each quadratic expression in the numerator and denominator.
- Cancel out common factors between the numerator and denominator.
After simplifying, the expression becomes (3)/(-x-4).