Final answer:
To simplify the given expression, factor the denominators and cancel out common factors between the fractions. The simplified form is 1/(x+2)(x-4).
Step-by-step explanation:
To simplify the expression (x+4)/(x²+5x+6) * (x+3)/(x²-16), we can factor the denominators and cancel out any common factors between them. The denominators are x²+5x+6 and x²-16.
Factoring them, we get (x+2)(x+3) and (x+4)(x-4), respectively.
Now, we can cancel out the common factor of (x+3) between the numerator of the first fraction and the denominator of the second fraction, and the common factor of (x+4) between the numerator of the second fraction and the denominator of the first fraction.
This leaves us with the simplified form of 1/(x+2)(x-4).