Multiply the following rational expr
\[
\frac{x^{2}+2 x-15}{x^{2}+(-4) x-12} \cdot \frac{x^{2}+8 x+12}{x^{2}-9}
\]
Answer
Finally, we multiply the remaining factors to get the final answer. The result of the multiplication of the given rational expressions is \(\boxed{\frac{(x + 5)(x + 6)}{(x - 6)(x + 3)}}\).
Step 1 ：Given the rational expressions \(\frac{x^{2}+2 x-15}{x^{2}+(-4) x-12}\) and \(\frac{x^{2}+8 x+12}{x^{2}-9}\), we are asked to multiply them.
Step 2 ：First, we factorize the numerators and denominators of the expressions. The factorized form of the expressions are \(\frac{(x - 3)(x + 5)}{(x - 6)(x + 2)}\) and \(\frac{(x + 2)(x + 6)}{(x - 3)(x + 3)}\).
Step 3 ：Next, we cancel out common factors from the numerator and denominator. After cancelling out, we get \(\frac{(x + 5)}{(x - 6)}\) and \(\frac{(x + 6)}{(x + 3)}\).
Step 4 ：Finally, we multiply the remaining factors to get the final answer. The result of the multiplication of the given rational expressions is \(\boxed{\frac{(x + 5)(x + 6)}{(x - 6)(x + 3)}}\).
