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 $\frac{6}{r^{2} + 1}$
35

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: $\frac{3 (r + 3)}{(r + 1) (r - 2)}$