2 What is the product of \( \frac{r^{2}-16}{r^{2}+4 r+3} \) and \( \frac{3 r+9}{r^{2}-2 r-8} ? \)
A \( \frac{r+5}{r^{2}+2 r-8} \)
B \( \frac{3 r+12}{r^{2}+3 r+2} \)
C \( \frac{12}{r+3} \)
D \( \frac{6}{r^{2}+1} \)
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Answer

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Answer

Cancel out common terms and simplify: \( \frac{3(r+3)}{(r+1)(r-2)} \)

Steps

Step 1 ：Factorize numerators and denominators: \( \frac{(r+4)(r-4)}{(r+1)(r+3)} \) and \( \frac{3(r+3)}{(r+4)(r-2)} \)

Step 2 ：Multiply both fractions: \( \frac{(r+4)(r-4)(r+3)}{(r+1)(r+3)(r+4)(r-2)} \) times \( \frac{3(r+3)}{(r+4)(r-2)} \)

Step 3 ：Cancel out common terms and simplify: \( \frac{3(r+3)}{(r+1)(r-2)} \)