Multiply the following rational expr
$\frac{x^{2} + 2 x - 15}{x^{2} + (- 4) x - 12} \cdot \frac{x^{2} + 8 x + 12}{x^{2} - 9}$

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Finally, we multiply the remaining factors to get the final answer. The result of the multiplication of the given rational expressions is $\frac{(x + 5) (x + 6)}{(x - 6) (x + 3)}$ .

Steps

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 $\frac{(x + 5) (x + 6)}{(x - 6) (x + 3)}$ .

Multiply the following rational exprx2+2x−15x2+(−4)x−12⋅x2+8x+12x2−9

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Multiply the following rational expr
$\frac{x^{2} + 2 x - 15}{x^{2} + (- 4) x - 12} \cdot \frac{x^{2} + 8 x + 12}{x^{2} - 9}$