Add as indicated. \( \frac{9}{x^{2}+4 x+4}+\frac{3}{x+2} \) Select the correct choice below and fill in the answer box(es) to complete your choice (Simplify your answer Use integers or fractions far any numbers in the expression Use a comma to separate anmwars as needed) A. \( \frac{9}{x^{2}+4 x+4}+\frac{3}{x+2}=\square \), no numbers must be excludod.
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To begin simplifying the expression \( \frac{9}{x^{2}+4 x+4}+\frac{3}{x+2} \), first note that \( x^{2}+4 x+4 \) can be factored into \( (x+2)^2 \). Therefore, we can rewrite the first part of the expression: \[ \frac{9}{(x+2)^2}+\frac{3}{x+2} \] Next, to combine these fractions, we need a common denominator, which will be \( (x+2)^2 \). The second fraction will need to be adjusted: \[ \frac{3}{x+2} = \frac{3(x+2)}{(x+2)^2} \] Now we can combine the fractions: \[ \frac{9 + 3(x+2)}{(x+2)^2} = \frac{9 + 3x + 6}{(x+2)^2} = \frac{3x + 15}{(x+2)^2} \] Finally, we can factor out a 3 from the numerator: \[ \frac{3(x + 5)}{(x + 2)^2} \] So, the simplified expression is: \[ \frac{3(x + 5)}{(x + 2)^2} \] The answer is: \[ A. \frac{3(x + 5)}{(x + 2)^2} \]
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