Final answer:
The expression (x^2 - 14x + 48) / (x^2 - 6x - 16) * (x^2 - 4) / (x^2 - 36) simplifies to (x - 6) / (x + 2) by factoring and canceling common factors.
Step-by-step explanation:
When simplifying the expression (x2 - 14x + 48) / (x2 - 6x - 16) * (x2 - 4) / (x2 - 36), we should first look for factors common to the numerators and the denominators to see if the expression can be simplified before multiplying.
First, factor each polynomial:
- (x2 - 14x + 48) factors to (x - 6)(x - 8)
- (x2 - 6x - 16) factors to (x - 8)(x + 2)
- (x2 - 4) factors to (x - 2)(x + 2), which is a difference of squares
- (x2 - 36) factors to (x - 6)(x + 6), also a difference of squares
The expression simplifies to:
((x - 6)(x - 8) / ((x - 8)(x + 2))) * ((x - 2)(x + 2) / ((x - 6)(x + 6))).
Next, cancel out the common factors in the numerator and denominator:
(x - 6) / (x + 2).
So, the simplified form of the given expression is (x - 6) / (x + 2).